Table of Contents

  • 0  Package Install
  • 1  Dataset: Iris (붓꽃 자료)
    • 1.1  Dataset with graphs
    • 1.2  Descriptive statistics of the datasetm
    • 1.3  Euclidean Distance of the dataset
  • 2  Weighted Maxcut
    • 2.1  Example: Fully Connected Graph with Randomized weight
    • 2.2  Brute Force Algorithms to Calculate Optimal Solution
  • 3  QAOA solving Weighted Maxcut
  • 4  Simulating with Different P-Values
  • 5  Clustering using QAOA-Weighted Maxcut with Iris Data
    • 5.1  Method 1: Brute Force Algorithms to Calculate Optimal Solution
    • 5.2  Method 2: QAOA
    • 5.3  Comparison with K-means Clustering
    • 5.4  Silhoutte Score
      • 5.4.1  Code with example
      • 5.4.2  Brute Force - Silhoutte Score
      • 5.4.3  QAOA - Silhoutte Score
      • 5.4.4  K-Means - Silhoutte Score
      • 5.4.5  True Label- Silhoutte Score
    • 5.5  Dunn Index
      • 5.5.1  Code with example
        • 5.5.1.1  클러스터 내 거리 측도 Intra-Cluster distance measure
        • 5.5.1.2  클러스터 간 거리 측도 Inter-Cluster distance measure
      • 5.5.2  Dunn Index 파이썬 구현
    • 5.6  Brute Force - Dunn Index
    • 5.7  QAOA - Dunn Index
    • 5.8  K-Means - Dunn Index
    • 5.9  True Label - Dunn Index

Package Install¶

In [1]:
# !pip install numpy
# !pip install pandas
# !pip install sklearn

# !pip install qiskit

Dataset: Iris (붓꽃 자료)¶

  • We then load the Iris data set. There is a bit of preprocessing to do in order to encode the inputs into the amplitudes of a quantum state. In the last preprocessing step, we translate the inputs x to rotation angles using the get_angles function we defined above.

Iris-Dataset-Classification.png

  • image source: https://www.embedded-robotics.com/iris-dataset-classification/

  • X variables: [Sepal length, Sepal width, Petal length, Petal width], (각 Sepal: 꽃받침, Petal: 꽃잎 의 가로, 세로 길이)

  • Y variable: Species of iris flowers (0:"setosa", 1:"versicolor", 2:"virginica")
  • We are trying to classify iris flowers to correct type of iris flowers using the lengths of various parts of the flower.
In [2]:
from sklearn.datasets import load_iris
import pandas as pd
import numpy as np

# visualization package
import matplotlib.pyplot as plt
import seaborn as sns

# sample data load
iris = load_iris()

# pring out data with variable types and its description
# print(iris)
In [3]:
# Description of the dataset
print(iris.DESCR)

.. _iris_dataset:

Iris plants dataset
--------------------

**Data Set Characteristics:**

    :Number of Instances: 150 (50 in each of three classes)
    :Number of Attributes: 4 numeric, predictive attributes and the class
    :Attribute Information:
        - sepal length in cm
        - sepal width in cm
        - petal length in cm
        - petal width in cm
        - class:
                - Iris-Setosa
                - Iris-Versicolour
                - Iris-Virginica
                
    :Summary Statistics:

    ============== ==== ==== ======= ===== ====================
                    Min  Max   Mean    SD   Class Correlation
    ============== ==== ==== ======= ===== ====================
    sepal length:   4.3  7.9   5.84   0.83    0.7826
    sepal width:    2.0  4.4   3.05   0.43   -0.4194
    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)
    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)
    ============== ==== ==== ======= ===== ====================

    :Missing Attribute Values: None
    :Class Distribution: 33.3% for each of 3 classes.
    :Creator: R.A. Fisher
    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
    :Date: July, 1988

The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken
from Fisher's paper. Note that it's the same as in R, but not as in the UCI
Machine Learning Repository, which has two wrong data points.

This is perhaps the best known database to be found in the
pattern recognition literature.  Fisher's paper is a classic in the field and
is referenced frequently to this day.  (See Duda & Hart, for example.)  The
data set contains 3 classes of 50 instances each, where each class refers to a
type of iris plant.  One class is linearly separable from the other 2; the
latter are NOT linearly separable from each other.

.. topic:: References

   - Fisher, R.A. "The use of multiple measurements in taxonomic problems"
     Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to
     Mathematical Statistics" (John Wiley, NY, 1950).
   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.
     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.
   - Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
     Structure and Classification Rule for Recognition in Partially Exposed
     Environments".  IEEE Transactions on Pattern Analysis and Machine
     Intelligence, Vol. PAMI-2, No. 1, 67-71.
   - Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule".  IEEE Transactions
     on Information Theory, May 1972, 431-433.
   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al"s AUTOCLASS II
     conceptual clustering system finds 3 classes in the data.
   - Many, many more ...

Dataset with graphs¶

In [4]:
# feature_names(x variables) 와 target(y variable)을 잘 나타내도록 data frame 생성
data_iris = pd.DataFrame(data=iris.data, columns=iris.feature_names)
data_iris['species'] = iris.target

# Mapping the labels-'species' with numbers
data_iris['species'] = data_iris['species'].map(
    {0: "setosa", 1: "versicolor", 2: "virginica"})
print(data_iris)

# Plot scatter plots and density distribution plots feature-wise WITH labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, hue="species", height=3)
plt.show()

     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \
0                  5.1               3.5                1.4               0.2   
1                  4.9               3.0                1.4               0.2   
2                  4.7               3.2                1.3               0.2   
3                  4.6               3.1                1.5               0.2   
4                  5.0               3.6                1.4               0.2   
..                 ...               ...                ...               ...   
145                6.7               3.0                5.2               2.3   
146                6.3               2.5                5.0               1.9   
147                6.5               3.0                5.2               2.0   
148                6.2               3.4                5.4               2.3   
149                5.9               3.0                5.1               1.8   

       species  
0       setosa  
1       setosa  
2       setosa  
3       setosa  
4       setosa  
..         ...  
145  virginica  
146  virginica  
147  virginica  
148  virginica  
149  virginica  

[150 rows x 5 columns]
In [5]:
# Plot scatter plots and density distribution plots feature-wise WITHOUT any labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, height=3)
plt.show()

Descriptive statistics of the datasetm¶

In [6]:
# Descriptive statistics of the dataset
data_iris.describe()
Out[6]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)
count 150.000000 150.000000 150.000000 150.000000
mean 5.843333 3.057333 3.758000 1.199333
std 0.828066 0.435866 1.765298 0.762238
min 4.300000 2.000000 1.000000 0.100000
25% 5.100000 2.800000 1.600000 0.300000
50% 5.800000 3.000000 4.350000 1.300000
75% 6.400000 3.300000 5.100000 1.800000
max 7.900000 4.400000 6.900000 2.500000
In [7]:
data_iris['species'].value_counts()

# pd.crosstab(index=data_iris['species'], columns="count")
Out[7]:
setosa        50
versicolor    50
virginica     50
Name: species, dtype: int64

Euclidean Distance of the dataset¶

In [8]:
# Calculate the Euclidean distance of the data
iris_euclidean_dist = np.linalg.norm(data_iris.iloc[:, 0:4].values, axis=1)
iris_euclidean_dist
Out[8]:
array([ 6.34507683,  5.91692488,  5.83609458,  5.7497826 ,  6.32139225,
        6.88621812,  5.8966092 ,  6.23297682,  5.45618915,  5.98999165,
        6.71863081,  6.09918027,  5.83180932,  5.35817133,  7.14982517,
        7.36613874,  6.79852925,  6.34901567,  7.06470098,  6.54140658,
        6.60681466,  6.48922183,  5.92958683,  6.32771681,  6.18465844,
        6.04979338,  6.26737585,  6.44825558,  6.37181293,  5.91016074,
        5.93717104,  6.56734345,  6.79043445,  7.06328535,  5.99249531,
        6.05970296,  6.65056389,  6.2401923 ,  5.48543526,  6.31347765,
        6.24739946,  5.22685374,  5.59732079,  6.33798075,  6.64981203,
        5.83866423,  6.56124988,  5.77927331,  6.63852393,  6.15548536,
        9.12633552,  8.58487041,  9.13673902,  7.29588925,  8.5732141 ,
        7.89113427,  8.67352293,  6.45445583,  8.64985549,  7.17635005,
        6.5       ,  7.98122798,  7.60526134,  8.3468557 ,  7.37699126,
        8.70746806,  7.92842986,  7.6642025 ,  8.11048704,  7.35051019,
        8.44570897,  7.92085854,  8.49705831,  8.28130425,  8.33966426,
        8.59534758,  8.89269363,  9.04322951,  8.1798533 ,  7.24568837,
        7.18748913,  7.12039325,  7.58814865,  8.47702778,  7.78845299,
        8.38868285,  8.87918915,  8.12588457,  7.67202711,  7.36138574,
        7.60328876,  8.32646384,  7.60526134,  6.49461315,  7.61445993,
        7.78267306,  7.76079893,  8.18718511,  6.5169011 ,  7.67007171,
        9.63483264,  8.39940474,  9.93126377,  9.09395404,  9.47259204,
       10.71120908,  7.30753036, 10.22888068,  9.38189746, 10.40480658,
        9.08295106,  8.94147639,  9.48156105,  8.23043134,  8.55862138,
        9.19673855,  9.20543318, 11.11125555, 10.90642013,  8.2516665 ,
        9.77905926,  8.19817053, 10.77125805,  8.61568337,  9.62704524,
       10.06578363,  8.51821578,  8.57088093,  9.19619487,  9.85088828,
       10.16956243, 11.03675677,  9.21954446,  8.70574523,  8.79147314,
       10.52568288,  9.4005319 ,  9.16842407,  8.44274837,  9.52837867,
        9.57183368,  9.40850679,  8.39940474,  9.8275124 ,  9.72213968,
        9.28547252,  8.63423419,  9.07138358,  9.18966811,  8.54751426])
In [9]:
# Create new column of Euclidean distance
data_iris['Euclid_dist'] = iris_euclidean_dist
data_iris['Euclid_dist_sq'] = iris_euclidean_dist**2
In [10]:
# # Function that calculates Mahalanobis distance
# def mahalanobis(x=None, data=None, cov=None):
#     x_mu = x - x.mean()
#     if not cov:
#         cov = np.cov(data.values.T)
#     inv_covmat = np.linalg.inv(cov)
#     left = np.dot(x_mu, inv_covmat)
#     mahal = np.dot(left, x_mu.T)
#     return mahal.diagonal()
In [11]:
# # Calculate the Mahalanobis distance of the data
# Mahal_dist = mahalanobis(x=data_iris.iloc[:,range(4)], data=data_iris.iloc[:,range(4)])
# Mahal_dist
In [12]:
# # Create new column of Mahalanobis distance
# data_iris['Mahal_dist'] = Mahal_dist
# data_iris['Mahal_dist_sq'] = Mahal_dist**2
In [13]:
data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq']]
# data_iris[['species', 'Euclid_dist','Euclid_dist_sq','Mahal_dist', 'Mahal_dist_sq']]
Out[13]:
species Euclid_dist Euclid_dist_sq
0 setosa 6.345077 40.26
1 setosa 5.916925 35.01
2 setosa 5.836095 34.06
3 setosa 5.749783 33.06
4 setosa 6.321392 39.96
... ... ... ...
145 virginica 9.285473 86.22
146 virginica 8.634234 74.55
147 virginica 9.071384 82.29
148 virginica 9.189668 84.45
149 virginica 8.547514 73.06

150 rows × 3 columns

In [14]:
# Plot scatter plots and density distribution plots feature-wise WITH labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, hue="species", height=3)
plt.show()
In [15]:
# Plot scatter plots and density distribution plots feature-wise WITHOUT any labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, height=3)
plt.show()
In [16]:
sns.pairplot(data_iris[['species', 'Euclid_dist',
             'Euclid_dist_sq']], hue="species", height=3)
# sns.pairplot(data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq', 'Mahal_dist','Mahal_dist_sq']], hue="species", height=3)
Out[16]:
<seaborn.axisgrid.PairGrid at 0x12d3b497430>
In [17]:
sns.pairplot(data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq']], height=3)
# sns.pairplot(data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq', 'Mahal_dist','Mahal_dist_sq']], height=3)
Out[17]:
<seaborn.axisgrid.PairGrid at 0x12d3b3b0490>
In [ ]:

Weighted Maxcut¶

Example: Fully Connected Graph with Randomized weight¶

In [18]:
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt


def draw_graph(G, col, pos):
    plt.figure(figsize=(12, 8))
    default_axes = plt.axes(frameon=True)
    nx.draw_networkx(G, node_color=col, node_size=600,
                     alpha=0.8, ax=default_axes, pos=pos, font_size=16)
    edge_labels = nx.get_edge_attributes(G, 'weight')
    nx.draw_networkx_edge_labels(
        G, pos=pos, edge_labels=edge_labels, font_size=16)


n = 6  # number of nodes in graph

np.random.seed(150)
edge_weights = np.random.randint(1, 5, size=(n, n))
edge_weights = edge_weights * edge_weights.T / 2

G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
for i in range(n):
    for j in range(n):
        if i > j:
            G.add_edge(i, j, weight=edge_weights[i, j])

colors = ['g' for node in G.nodes()]
pos = nx.spring_layout(G)
In [19]:
# graph G: nodes
G.nodes
Out[19]:
NodeView((0, 1, 2, 3, 4, 5))
In [20]:
# graph G: edges
G.edges
Out[20]:
EdgeView([(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)])
In [21]:
# graph G: edges with weights
G.edges.data()
Out[21]:
EdgeDataView([(0, 1, {'weight': 1.5}), (0, 2, {'weight': 6.0}), (0, 3, {'weight': 1.0}), (0, 4, {'weight': 0.5}), (0, 5, {'weight': 3.0}), (1, 2, {'weight': 6.0}), (1, 3, {'weight': 3.0}), (1, 4, {'weight': 2.0}), (1, 5, {'weight': 2.0}), (2, 3, {'weight': 0.5}), (2, 4, {'weight': 4.0}), (2, 5, {'weight': 4.0}), (3, 4, {'weight': 2.0}), (3, 5, {'weight': 4.0}), (4, 5, {'weight': 6.0})])
In [22]:
# Plot of the give graph G
draw_graph(G, colors, pos)
In [23]:
# Adjacency matrix of weighted graph
w = np.zeros([n, n])
for i in range(n):
    for j in range(n):
        temp = G.get_edge_data(i, j, default=0)
        if temp != 0:
            w[i, j] = temp['weight']

w
Out[23]:
array([[0. , 1.5, 6. , 1. , 0.5, 3. ],
       [1.5, 0. , 6. , 3. , 2. , 2. ],
       [6. , 6. , 0. , 0.5, 4. , 4. ],
       [1. , 3. , 0.5, 0. , 2. , 4. ],
       [0.5, 2. , 4. , 2. , 0. , 6. ],
       [3. , 2. , 4. , 4. , 6. , 0. ]])

Brute Force Algorithms to Calculate Optimal Solution¶

In [24]:
best_cost_brute = 0
for b in range(2**n):
    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
    cost = 0
    for i in range(n):
        for j in range(n):
            cost = cost + w[i, j] * x[i] * (1-x[j])
    if best_cost_brute < cost:
        best_cost_brute = cost
        xbest_brute = x
    print('case =', '%-20s' % str(x), ' cost =', '%-6s' %
          str(cost), ' try =', str(b+1))

colors_brute = ['g' if xbest_brute[i] == 0 else 'c' for i in range(n)]
print('\nBest case(solution) =', '%-20s' %
      str(xbest_brute), ' cost =', '%-6s' % str(best_cost_brute))

case = [0, 0, 0, 0, 0, 0]    cost = 0.0     try = 1
case = [1, 0, 0, 0, 0, 0]    cost = 12.0    try = 2
case = [0, 1, 0, 0, 0, 0]    cost = 14.5    try = 3
case = [1, 1, 0, 0, 0, 0]    cost = 23.5    try = 4
case = [0, 0, 1, 0, 0, 0]    cost = 20.5    try = 5
case = [1, 0, 1, 0, 0, 0]    cost = 20.5    try = 6
case = [0, 1, 1, 0, 0, 0]    cost = 23.0    try = 7
case = [1, 1, 1, 0, 0, 0]    cost = 20.0    try = 8
case = [0, 0, 0, 1, 0, 0]    cost = 10.5    try = 9
case = [1, 0, 0, 1, 0, 0]    cost = 20.5    try = 10
case = [0, 1, 0, 1, 0, 0]    cost = 19.0    try = 11
case = [1, 1, 0, 1, 0, 0]    cost = 26.0    try = 12
case = [0, 0, 1, 1, 0, 0]    cost = 30.0    try = 13
case = [1, 0, 1, 1, 0, 0]    cost = 28.0    try = 14
case = [0, 1, 1, 1, 0, 0]    cost = 26.5    try = 15
case = [1, 1, 1, 1, 0, 0]    cost = 21.5    try = 16
case = [0, 0, 0, 0, 1, 0]    cost = 14.5    try = 17
case = [1, 0, 0, 0, 1, 0]    cost = 25.5    try = 18
case = [0, 1, 0, 0, 1, 0]    cost = 25.0    try = 19
case = [1, 1, 0, 0, 1, 0]    cost = 33.0    try = 20
case = [0, 0, 1, 0, 1, 0]    cost = 27.0    try = 21
case = [1, 0, 1, 0, 1, 0]    cost = 26.0    try = 22
case = [0, 1, 1, 0, 1, 0]    cost = 25.5    try = 23
case = [1, 1, 1, 0, 1, 0]    cost = 21.5    try = 24
case = [0, 0, 0, 1, 1, 0]    cost = 21.0    try = 25
case = [1, 0, 0, 1, 1, 0]    cost = 30.0    try = 26
case = [0, 1, 0, 1, 1, 0]    cost = 25.5    try = 27
case = [1, 1, 0, 1, 1, 0]    cost = 31.5    try = 28
case = [0, 0, 1, 1, 1, 0]    cost = 32.5    try = 29
case = [1, 0, 1, 1, 1, 0]    cost = 29.5    try = 30
case = [0, 1, 1, 1, 1, 0]    cost = 25.0    try = 31
case = [1, 1, 1, 1, 1, 0]    cost = 19.0    try = 32
case = [0, 0, 0, 0, 0, 1]    cost = 19.0    try = 33
case = [1, 0, 0, 0, 0, 1]    cost = 25.0    try = 34
case = [0, 1, 0, 0, 0, 1]    cost = 29.5    try = 35
case = [1, 1, 0, 0, 0, 1]    cost = 32.5    try = 36
case = [0, 0, 1, 0, 0, 1]    cost = 31.5    try = 37
case = [1, 0, 1, 0, 0, 1]    cost = 25.5    try = 38
case = [0, 1, 1, 0, 0, 1]    cost = 30.0    try = 39
case = [1, 1, 1, 0, 0, 1]    cost = 21.0    try = 40
case = [0, 0, 0, 1, 0, 1]    cost = 21.5    try = 41
case = [1, 0, 0, 1, 0, 1]    cost = 25.5    try = 42
case = [0, 1, 0, 1, 0, 1]    cost = 26.0    try = 43
case = [1, 1, 0, 1, 0, 1]    cost = 27.0    try = 44
case = [0, 0, 1, 1, 0, 1]    cost = 33.0    try = 45
case = [1, 0, 1, 1, 0, 1]    cost = 25.0    try = 46
case = [0, 1, 1, 1, 0, 1]    cost = 25.5    try = 47
case = [1, 1, 1, 1, 0, 1]    cost = 14.5    try = 48
case = [0, 0, 0, 0, 1, 1]    cost = 21.5    try = 49
case = [1, 0, 0, 0, 1, 1]    cost = 26.5    try = 50
case = [0, 1, 0, 0, 1, 1]    cost = 28.0    try = 51
case = [1, 1, 0, 0, 1, 1]    cost = 30.0    try = 52
case = [0, 0, 1, 0, 1, 1]    cost = 26.0    try = 53
case = [1, 0, 1, 0, 1, 1]    cost = 19.0    try = 54
case = [0, 1, 1, 0, 1, 1]    cost = 20.5    try = 55
case = [1, 1, 1, 0, 1, 1]    cost = 10.5    try = 56
case = [0, 0, 0, 1, 1, 1]    cost = 20.0    try = 57
case = [1, 0, 0, 1, 1, 1]    cost = 23.0    try = 58
case = [0, 1, 0, 1, 1, 1]    cost = 20.5    try = 59
case = [1, 1, 0, 1, 1, 1]    cost = 20.5    try = 60
case = [0, 0, 1, 1, 1, 1]    cost = 23.5    try = 61
case = [1, 0, 1, 1, 1, 1]    cost = 14.5    try = 62
case = [0, 1, 1, 1, 1, 1]    cost = 12.0    try = 63
case = [1, 1, 1, 1, 1, 1]    cost = 0.0     try = 64

Best case(solution) = [1, 1, 0, 0, 1, 0]    cost = 33.0
In [25]:
draw_graph(G, colors_brute, pos)

QAOA solving Weighted Maxcut¶

In [26]:
from qiskit import QuantumCircuit, Aer
from qiskit.circuit import Parameter


def maxcut_obj(solution, graph):
    obj = 0
    for i, j in graph.edges():
        if solution[i] != solution[j]:
            obj -= 1 * w[i][j]
    return obj  # cost function(hamiltonian)


def compute_expectation(counts, graph):
    avg = 0
    sum_count = 0
    for bit_string, count in counts.items():
        obj = maxcut_obj(bit_string, graph)
        avg += obj * count
        sum_count += count  # sum_count is shot
    return avg/sum_count  # minimize this function


def create_qaoa_circ(graph, theta):
    nqubits = len(graph.nodes())
    n_layers = len(theta)//2
    beta = theta[:n_layers]
    gamma = theta[n_layers:]

    qc = QuantumCircuit(nqubits)

    qc.h(range(nqubits))

    for layer_index in range(n_layers):
        for pair in list(graph.edges()):
            qc.rzz(2 * gamma[layer_index] * w[pair[0]]
                   [pair[1]], pair[0], pair[1])
        for qubit in range(nqubits):
            qc.rx(2 * beta[layer_index], qubit)

    qc.measure_all()
    return qc


def get_expectation(graph, shots=512):
    backend = Aer.get_backend('qasm_simulator')
    backend.shots = shots

    def execute_circ(theta):
        qc = create_qaoa_circ(graph, theta)
        counts = backend.run(qc, seed_simulator=10,
                             nshots=512).result().get_counts()
        return compute_expectation(counts, graph)

    return execute_circ
In [27]:
from scipy.optimize import minimize
expectation = get_expectation(G)
p = 1  # 32 64
res = minimize(expectation, np.ones(p*2)*np.pi/2,
               method='COBYLA', options={'maxiter': 2500})
In [28]:
res
Out[28]:
     fun: -24.17529296875
   maxcv: 0.0
 message: 'Optimization terminated successfully.'
    nfev: 31
  status: 1
 success: True
       x: array([2.57910398, 1.5991255 ])
In [29]:
from qiskit.visualization import plot_histogram
backend = Aer.get_backend('aer_simulator')
backend.shots = 2**14

qc_res = create_qaoa_circ(G, res.x)
counts = backend.run(qc_res, seed_simulator=10).result().get_counts()
plot_histogram(counts, figsize=(20, 5), title='512 Shots')
Out[29]:
In [30]:
# Plot the Quantum Circuit of QAOA
# qc_res.draw(output='mpl', plot_barriers=True).savefig('QAOA_circuit.png', dpi=720)
qc_res.draw(output='mpl', plot_barriers=True)
Out[30]:
In [31]:
# qc_res.draw(output='mpl', plot_barriers=True, fold=-1).savefig('QAOA_circuit(full).png', dpi=720)
qc_res.draw(output='mpl', plot_barriers=True, fold=-1)
Out[31]:
In [32]:
str(counts)
Out[32]:
"{'001001': 54, '100001': 23, '001010': 15, '111111': 3, '101001': 79, '111010': 82, '001000': 16, '101000': 30, '011011': 22, '011110': 27, '000001': 2, '110110': 67, '010111': 23, '101100': 1, '000011': 6, '011111': 8, '110010': 16, '101110': 2, '000101': 67, '010001': 5, '001110': 4, '111011': 21, '100101': 65, '010110': 75, '110011': 3, '000100': 16, '101101': 8, '000111': 8, '100100': 25, '111100': 5, '001101': 34, '010010': 9, '101111': 5, '000110': 4, '110001': 13, '011010': 62, '100000': 8, '000000': 6, '110111': 12, '001100': 2, '100011': 12, '100111': 13, '011000': 9, '111000': 6, '000010': 3, '110101': 16, '101011': 2, '111001': 10, '010000': 5, '001011': 1, '111110': 3, '010011': 4, '010100': 1, '011100': 5, '010101': 1}"
In [33]:
# Sort the counted shot results
{k: v for k, v in sorted(counts.items(), key=lambda item: item[1])}
Out[33]:
{'101100': 1,
 '001011': 1,
 '010100': 1,
 '010101': 1,
 '000001': 2,
 '101110': 2,
 '001100': 2,
 '101011': 2,
 '111111': 3,
 '110011': 3,
 '000010': 3,
 '111110': 3,
 '001110': 4,
 '000110': 4,
 '010011': 4,
 '010001': 5,
 '111100': 5,
 '101111': 5,
 '010000': 5,
 '011100': 5,
 '000011': 6,
 '000000': 6,
 '111000': 6,
 '011111': 8,
 '101101': 8,
 '000111': 8,
 '100000': 8,
 '010010': 9,
 '011000': 9,
 '111001': 10,
 '110111': 12,
 '100011': 12,
 '110001': 13,
 '100111': 13,
 '001010': 15,
 '001000': 16,
 '110010': 16,
 '000100': 16,
 '110101': 16,
 '111011': 21,
 '011011': 22,
 '100001': 23,
 '010111': 23,
 '100100': 25,
 '011110': 27,
 '101000': 30,
 '001101': 34,
 '001001': 54,
 '011010': 62,
 '100101': 65,
 '110110': 67,
 '000101': 67,
 '010110': 75,
 '101001': 79,
 '111010': 82}
In [34]:
result_col = list(map(int, list(max(counts, key=counts.get))))
result_colors = ['g' if result_col[i] == 0 else 'c' for i in range(n)]
In [35]:
# Result of Brute Force algorithm
draw_graph(G, colors_brute, pos)
In [36]:
# Result of QAOA
draw_graph(G, result_colors, pos)
In [37]:
print('xbest_brute :', xbest_brute)
print('QAOA        :', result_col)

xbest_brute : [1, 1, 0, 0, 1, 0]
QAOA        : [1, 1, 1, 0, 1, 0]
In [ ]:

Simulating with Different P-Values¶

  • p is just an iteration number, where we perform repetative works and trying to find the best solution out of iteratively executed results.
In [38]:
from tqdm import tqdm

p = 16
res = []
for i in tqdm(range(1, p+1)):
    res.append(minimize(expectation, np.ones(i*2)*np.pi/2,
               method='COBYLA', options={'maxiter': 2500}))

100%|██████████| 16/16 [00:23<00:00,  1.44s/it]
In [39]:
res[0:2]
Out[39]:
[     fun: -24.17529296875
    maxcv: 0.0
  message: 'Optimization terminated successfully.'
     nfev: 31
   status: 1
  success: True
        x: array([2.57910398, 1.5991255 ]),
      fun: -24.716796875
    maxcv: 0.0
  message: 'Optimization terminated successfully.'
     nfev: 54
   status: 1
  success: True
        x: array([2.52461869, 1.63875349, 1.61624568, 1.52923708])]
In [40]:
approx = []
for i in range(p):
    approx.append(-res[i].fun/best_cost_brute)

x = np.arange(1, p+1, 1)

plt.figure(figsize=(8, 6))
plt.plot(x, approx, marker='o', markersize=6, c='k', linestyle='--')
plt.ylim((0.5, 1))
plt.xlim(0, p)
plt.xlabel('iteration')
plt.ylabel('Approximation')
plt.grid(True)
plt.show()
In [41]:
best_p = np.argmax(approx)
print("The best p(iterationo number) is", best_p)

The best p(iterationo number) is 11
  • When p=25, cost hamiltonian is optimized. So we use the best optimized values to output our results.
In [42]:
res[best_p].x
Out[42]:
array([2.69931677, 1.70145888, 1.83501131, 1.52640593, 1.70235575,
       1.52533461, 1.53010659, 1.94876412, 1.40228443, 1.54544357,
       1.47815615, 1.48456692, 1.58893494, 1.57102304, 1.58103879,
       1.68907833, 1.40984573, 1.6220806 , 1.63468791, 1.62148146,
       1.52878007, 1.70463034, 1.58593247, 1.60855217])
In [43]:
from qiskit.visualization import plot_histogram
backend = Aer.get_backend('aer_simulator')
backend.shots = 512

qc_res = create_qaoa_circ(G, res[best_p].x)
counts = backend.run(qc_res, seed_simulator=10).result().get_counts()
plot_histogram(counts, figsize=(20, 5), title='512 Shots')
Out[43]:
In [44]:
result_col = list(map(int, list(max(counts, key=counts.get))))
result_colors = ['g' if result_col[i] == 0 else 'c' for i in range(n)]
In [45]:
print('xbest_brute :', xbest_brute)
print('QAOA        :', result_col)

xbest_brute : [1, 1, 0, 0, 1, 0]
QAOA        : [1, 1, 0, 0, 1, 0]
In [46]:
draw_graph(G, colors_brute, pos)
In [47]:
draw_graph(G, result_colors, pos)
In [48]:
print('Best solution - Brute Force : ' +
      str(xbest_brute) + ',  cost = ' + str(best_cost_brute))
print('Best solution - QAOA        : ' + str(result_col) +
      ',  cost = ' + str(-res[best_p].fun))

Best solution - Brute Force : [1, 1, 0, 0, 1, 0],  cost = 33.0
Best solution - QAOA        : [1, 1, 0, 0, 1, 0],  cost = 28.9130859375
In [ ]:

Clustering using QAOA-Weighted Maxcut with Iris Data¶

In [49]:
data_iris
Out[49]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm) species Euclid_dist Euclid_dist_sq
0 5.1 3.5 1.4 0.2 setosa 6.345077 40.26
1 4.9 3.0 1.4 0.2 setosa 5.916925 35.01
2 4.7 3.2 1.3 0.2 setosa 5.836095 34.06
3 4.6 3.1 1.5 0.2 setosa 5.749783 33.06
4 5.0 3.6 1.4 0.2 setosa 6.321392 39.96
... ... ... ... ... ... ... ...
145 6.7 3.0 5.2 2.3 virginica 9.285473 86.22
146 6.3 2.5 5.0 1.9 virginica 8.634234 74.55
147 6.5 3.0 5.2 2.0 virginica 9.071384 82.29
148 6.2 3.4 5.4 2.3 virginica 9.189668 84.45
149 5.9 3.0 5.1 1.8 virginica 8.547514 73.06

150 rows × 7 columns

  • Selected 3 datapoint of each from the different labels, total of 9 datapoints
In [50]:
num_sample1 = 4
num_sample2 = 8

sample_df1 = data_iris[data_iris['species'] ==
                       'setosa'].sample(num_sample1).sort_index()
# sample_df2 = data_iris[data_iris['species'] =='versicolor'].sample(num_sample).sort_index()
sample_df3 = data_iris[data_iris['species'] ==
                       'virginica'].sample(num_sample2).sort_index()

# data_iris_sample = pd.concat([sample_df1, sample_df2, sample_df3])
data_iris_sample = pd.concat([sample_df1, sample_df3])
data_iris_sample
Out[50]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm) species Euclid_dist Euclid_dist_sq
14 5.8 4.0 1.2 0.2 setosa 7.149825 51.12
15 5.7 4.4 1.5 0.4 setosa 7.366139 54.26
27 5.2 3.5 1.5 0.2 setosa 6.448256 41.58
33 5.5 4.2 1.4 0.2 setosa 7.063285 49.89
114 5.8 2.8 5.1 2.4 virginica 8.558621 73.25
117 7.7 3.8 6.7 2.2 virginica 11.111256 123.46
118 7.7 2.6 6.9 2.3 virginica 10.906420 118.95
125 7.2 3.2 6.0 1.8 virginica 10.065784 101.32
126 6.2 2.8 4.8 1.8 virginica 8.518216 72.56
130 7.4 2.8 6.1 1.9 virginica 10.169562 103.42
140 6.7 3.1 5.6 2.4 virginica 9.571834 91.62
141 6.9 3.1 5.1 2.3 virginica 9.408507 88.52
In [51]:
data_iris_qaoa = data_iris_sample[[
    'sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']]
data_iris_qaoa = np.array(data_iris_qaoa)
data_iris_qaoa_label = iris.target[data_iris_sample.index]
In [52]:
data_iris_qaoa
Out[52]:
array([[5.8, 4. , 1.2, 0.2],
       [5.7, 4.4, 1.5, 0.4],
       [5.2, 3.5, 1.5, 0.2],
       [5.5, 4.2, 1.4, 0.2],
       [5.8, 2.8, 5.1, 2.4],
       [7.7, 3.8, 6.7, 2.2],
       [7.7, 2.6, 6.9, 2.3],
       [7.2, 3.2, 6. , 1.8],
       [6.2, 2.8, 4.8, 1.8],
       [7.4, 2.8, 6.1, 1.9],
       [6.7, 3.1, 5.6, 2.4],
       [6.9, 3.1, 5.1, 2.3]])
In [53]:
data_iris_qaoa_label
Out[53]:
array([0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2])
In [54]:
len(data_iris_qaoa_label)
Out[54]:
12

Method 1: Brute Force Algorithms to Calculate Optimal Solution¶

In [55]:
# Function to calculate the distance between given two data points

import math


def dist(a, b):
    "Euclidean dist between two lists"
    d = np.linalg.norm(np.array(a) - np.array(b), axis=0)
    return round(d, 4)
In [56]:
import random

# Assign the number of nodes, edge connection, and its weight of the Graph.
n = len(data_iris_qaoa_label)
data = data_iris_qaoa
label = data_iris_qaoa_label

datapoints = data.tolist()
print("Data points:", datapoints)
labels = label
print("Data labels:", labels)

G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
for i in range(n):
    for j in range(n):
        if i > j:
            G.add_edge(i, j, weight=dist(datapoints[i], datapoints[j]))

colors = ['g' for node in G.nodes()]
pos = nx.spring_layout(G)

Data points: [[5.8, 4.0, 1.2, 0.2], [5.7, 4.4, 1.5, 0.4], [5.2, 3.5, 1.5, 0.2], [5.5, 4.2, 1.4, 0.2], [5.8, 2.8, 5.1, 2.4], [7.7, 3.8, 6.7, 2.2], [7.7, 2.6, 6.9, 2.3], [7.2, 3.2, 6.0, 1.8], [6.2, 2.8, 4.8, 1.8], [7.4, 2.8, 6.1, 1.9], [6.7, 3.1, 5.6, 2.4], [6.9, 3.1, 5.1, 2.3]]
Data labels: [0 0 0 0 2 2 2 2 2 2 2 2]
In [57]:
draw_graph(G, colors, pos)
In [58]:
# Calculate Adjacency matrix of the given Graph
w = np.zeros([n, n])
for i in range(n):
    for j in range(n):
        temp = G.get_edge_data(i, j, default=0)
        if temp != 0:
            w[i, j] = temp['weight']

w
Out[58]:
array([[0.    , 0.5477, 0.8367, 0.4123, 4.6357, 6.1563, 6.5169, 5.3104,
        4.1376, 5.5588, 5.0813, 4.6519],
       [0.5477, 0.    , 1.0488, 0.3606, 4.4193, 5.8856, 6.3253, 5.0892,
        3.9573, 5.3722, 4.8477, 4.4385],
       [0.8367, 1.0488, 0.    , 0.7681, 4.3186, 6.1139, 6.3742, 5.1865,
        3.8652, 5.4203, 4.9051, 4.5188],
       [0.4123, 0.3606, 0.7681, 0.    , 4.5365, 6.0902, 6.4854, 5.2545,
        4.0706, 5.5272, 5.013 , 4.6119],
       [4.6357, 4.4193, 4.3186, 4.5365, 0.    , 2.6851, 2.6268, 1.8138,
        0.781 , 1.9519, 1.0724, 1.1446],
       [6.1563, 5.8856, 6.1139, 6.0902, 2.6851, 0.    , 1.2207, 1.1225,
        2.6495, 1.241 , 1.6553, 1.9235],
       [6.5169, 6.3253, 6.3742, 6.4854, 2.6268, 1.2207, 0.    , 1.2923,
        2.6363, 0.9644, 1.7176, 2.0322],
       [5.3104, 5.0892, 5.1865, 5.2545, 1.8138, 1.1225, 1.2923, 0.    ,
        1.6125, 0.469 , 0.8832, 1.077 ],
       [4.1376, 3.9573, 3.8652, 4.0706, 0.781 , 2.6495, 2.6363, 1.6125,
        0.    , 1.772 , 1.1576, 0.9592],
       [5.5588, 5.3722, 5.4203, 5.5272, 1.9519, 1.241 , 0.9644, 0.469 ,
        1.772 , 0.    , 1.0392, 1.2247],
       [5.0813, 4.8477, 4.9051, 5.013 , 1.0724, 1.6553, 1.7176, 0.8832,
        1.1576, 1.0392, 0.    , 0.5477],
       [4.6519, 4.4385, 4.5188, 4.6119, 1.1446, 1.9235, 2.0322, 1.077 ,
        0.9592, 1.2247, 0.5477, 0.    ]])
  • Brute Force Algorithm
In [59]:
best_cost_brute = 0
for b in range(2**n):
    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
    cost = 0
    for i in range(n):
        for j in range(n):
            cost = cost + w[i, j] * x[i] * (1-x[j])
    if best_cost_brute < cost:
        best_cost_brute = cost
        xbest_brute = x
    print('case =', '%-30s' % str(x), ' cost =', '%-24s' %
          str(cost), 'try =', str(b+1))

colors_brute = ['g' if xbest_brute[i] == 0 else 'c' for i in range(n)]
print('\nBest case(solution) =', '%-30s' %
      str(xbest_brute), ' cost =', '%-24s' % str(best_cost_brute))

case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 0.0                      try = 1
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 43.84559999999999        try = 2
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 42.2922                  try = 3
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 85.04240000000001        try = 4
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 43.356199999999994       try = 5
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 85.52839999999999        try = 6
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 83.5508                  try = 7
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 124.62760000000002       try = 8
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 43.1303                  try = 9
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 86.15129999999999        try = 10
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 84.7013                  try = 11
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 126.62690000000003       try = 12
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 84.9503                  try = 13
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 126.2979                 try = 14
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 124.4237                 try = 15
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 164.6759                 try = 16
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 29.985699999999998       try = 17
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 64.5599                  try = 18
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 63.439299999999996       try = 19
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 96.91810000000001        try = 20
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 64.7047                  try = 21
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 97.60550000000002        try = 22
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 96.06070000000001        try = 23
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 127.86610000000002       try = 24
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 64.043                   try = 25
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 97.79260000000002        try = 26
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 96.77540000000002        try = 27
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 129.42960000000002       try = 28
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 97.22580000000002        try = 29
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 129.30200000000002       try = 30
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 127.86060000000002       try = 31
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 158.8414                 try = 32
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 36.743599999999994       try = 33
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 68.27660000000002        try = 34
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 67.26460000000002        try = 35
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 97.70219999999999        try = 36
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 67.87200000000001        try = 37
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 97.73159999999999        try = 38
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 96.2954                  try = 39
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 125.0596                 try = 40
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 67.6935                  try = 41
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 98.4019                  try = 42
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 97.49330000000002        try = 43
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 127.1063                 try = 44
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 97.28570000000002        try = 45
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 126.3207                 try = 46
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 124.98790000000001       try = 47
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 152.9275                 try = 48
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 61.359100000000005       try = 49
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 83.6207                  try = 50
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 83.04150000000001        try = 51
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 104.20769999999999       try = 52
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 83.8503                  try = 53
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 104.43849999999999       try = 54
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 103.4351                 try = 55
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 122.9279                 try = 56
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 83.236                   try = 57
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 104.67299999999999       try = 58
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 104.1972                 try = 59
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 124.53879999999998       try = 60
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 104.191                  try = 61
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 123.95459999999999       try = 62
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 123.05460000000002       try = 63
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 141.72279999999998       try = 64
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 38.192099999999996       try = 65
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 69.0039                  try = 66
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 67.83370000000001        try = 67
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 97.55009999999999        try = 68
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 68.79990000000001        try = 69
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 97.93829999999998        try = 70
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 96.3439                  try = 71
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 124.3869                 try = 72
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 68.3516                  try = 73
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 98.3388                  try = 74
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 97.272                   try = 75
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 126.1638                 try = 76
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 97.42320000000002        try = 77
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 125.73700000000001       try = 78
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 124.246                  try = 79
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 151.4644                 try = 80
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 62.92419999999999        try = 81
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 84.46459999999999        try = 82
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 83.72720000000001        try = 83
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 104.17219999999999       try = 84
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 84.8948                  try = 85
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 104.76180000000001       try = 86
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 103.60020000000002       try = 87
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 122.3718                 try = 88
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 84.0107                  try = 89
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 104.7265                 try = 90
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 104.09250000000002       try = 91
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 123.7129                 try = 92
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 104.44509999999998       try = 93
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 123.4875                 try = 94
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 122.42930000000003       try = 95
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 140.37630000000001       try = 96
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 72.49430000000001        try = 97
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 90.99350000000001        try = 98
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 90.36470000000001        try = 99
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 107.7685                 try = 100
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 90.8743                  try = 101
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 107.7001                 try = 102
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 106.64710000000001       try = 103
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 122.37750000000001       try = 104
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 90.47340000000001        try = 105
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 108.14800000000002       try = 106
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 107.62260000000002       try = 107
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 124.2018                 try = 108
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 107.3172                 try = 109
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 123.31840000000003       try = 110
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 122.36880000000004       try = 111
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 137.27460000000002       try = 112
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 91.85620000000002        try = 113
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 101.084                  try = 114
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 100.88800000000002       try = 115
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 109.02040000000001       try = 116
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 101.599                  try = 117
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 109.1534                 try = 118
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 108.53320000000001       try = 119
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 114.99220000000001       try = 120
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 100.76230000000002       try = 121
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 109.16550000000001       try = 122
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 109.07290000000002       try = 123
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 116.38070000000002       try = 124
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 108.9689                 try = 125
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 115.6987                 try = 126
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 115.18190000000003       try = 127
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 120.81630000000003       try = 128
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 29.1109                  try = 129
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 62.335699999999996       try = 130
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 61.2247                  try = 131
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 93.35409999999999        try = 132
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 62.0941                  try = 133
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 93.6455                  try = 134
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 92.1103                  try = 135
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 122.56630000000001       try = 136
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 61.7322                  try = 137
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 94.13239999999999        try = 138
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 93.1248                  try = 139
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 124.42960000000001       try = 140
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 93.17920000000001        try = 141
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 123.906                  try = 142
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 122.4742                 try = 143
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 152.10559999999998       try = 144
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 55.468999999999994       try = 145
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 79.4224                  try = 146
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 78.74419999999999        try = 147
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 101.6022                 try = 148
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 79.81499999999998        try = 149
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 102.09500000000001       try = 150
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 100.9926                 try = 151
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 122.17719999999998       try = 152
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 79.01729999999999        try = 153
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 102.14609999999999       try = 154
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 101.5713                 try = 155
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 123.6047                 try = 156
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 101.82710000000002       try = 157
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 123.2825                 try = 158
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 122.2835                 try = 159
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 142.6435                 try = 160
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 63.60949999999999        try = 161
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 84.52169999999998        try = 162
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 83.95209999999997        try = 163
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 103.76889999999997       try = 164
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 84.3649                  try = 165
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 103.60369999999998       try = 166
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 102.60989999999998       try = 167
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 120.7533                 try = 168
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 84.05039999999998        try = 169
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 104.13799999999999       try = 170
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 103.67179999999998       try = 171
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 122.66399999999997       try = 172
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 103.26959999999998       try = 173
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 121.68379999999999       try = 174
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 120.79339999999999       try = 175
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 138.11219999999997       try = 176
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 84.59739999999998        try = 177
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 96.23819999999999        try = 178
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 96.1014                  try = 179
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 106.64679999999997       try = 180
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 96.71559999999998        try = 181
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 106.68299999999998       try = 182
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 106.12199999999997       try = 183
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 114.99399999999999       try = 184
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 95.96529999999998        try = 185
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 106.78149999999998       try = 186
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 106.74809999999998       try = 187
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 116.46889999999998       try = 188
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 106.54729999999999       try = 189
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 115.69009999999999       try = 190
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 115.2325                 try = 191
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 123.2799                 try = 192
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 64.7184                  try = 193
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 84.90939999999999        try = 194
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 84.18159999999999        try = 195
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 103.27719999999998       try = 196
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 84.9532                  try = 197
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 103.47080000000001       try = 198
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 102.3188                 try = 199
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 119.741                  try = 200
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 84.3689                  try = 201
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 103.7353                 try = 202
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 103.11089999999999       try = 203
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 121.3819                 try = 204
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 103.06750000000001       try = 205
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 120.7605                 try = 206
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 119.71189999999999       try = 207
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 136.30949999999999       try = 208
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 85.82289999999998        try = 209
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 96.7425                  try = 210
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 96.44749999999999        try = 211
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 106.27170000000001       try = 212
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 97.4205                  try = 213
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 106.66669999999999       try = 214
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 105.94749999999999       try = 215
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 114.0983                 try = 216
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 96.40039999999999        try = 217
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 106.4954                 try = 218
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 106.30380000000001       try = 219
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 115.30340000000001       try = 220
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 106.4618                 try = 221
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 114.88340000000001       try = 222
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 114.2676                 try = 223
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 121.59380000000002       try = 224
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 96.77559999999998        try = 225
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 104.65400000000001       try = 226
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 104.46759999999999       try = 227
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 111.2506                 try = 228
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 104.78260000000002       try = 229
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 110.9876                 try = 230
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 110.377                  try = 231
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 115.48660000000002       try = 232
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 104.24570000000001       try = 233
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 111.29950000000002       try = 234
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 111.2165                 try = 235
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 117.17490000000001       try = 236
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 110.71650000000002       try = 237
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 116.0969                 try = 238
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 115.58970000000002       try = 239
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 119.87470000000002       try = 240
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 112.50990000000002       try = 241
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 111.11690000000002       try = 242
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 111.36330000000001       try = 243
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 108.8749                 try = 244
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 111.87969999999999       try = 245
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 108.8133                 try = 246
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 108.63550000000001       try = 247
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 104.47369999999998       try = 248
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 110.907                  try = 249
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 108.6894                 try = 250
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 109.03920000000001       try = 251
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 105.72619999999999       try = 252
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 108.74060000000001       try = 253
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 104.8496                 try = 254
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 104.7752                 try = 255
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 99.78880000000001        try = 256
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 27.598799999999994       try = 257
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 63.16919999999999        try = 258
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 61.9764                  try = 259
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 96.4514                  try = 260
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 63.224599999999995       try = 261
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 97.12160000000002        try = 262
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 95.50460000000002        try = 263
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 128.30620000000002       try = 264
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 62.587900000000005       try = 265
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 97.33370000000002        try = 266
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 96.24430000000002        try = 267
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 129.89470000000003       try = 268
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 96.67750000000002        try = 269
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 129.74990000000005       try = 270
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 128.23630000000003       try = 271
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 160.21330000000003       try = 272
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 56.0225                  try = 273
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 82.32150000000001        try = 274
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 81.56150000000001        try = 275
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 106.76510000000002       try = 276
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 83.01110000000003        try = 277
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 107.63670000000002       try = 278
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 106.45250000000001       try = 279
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 129.98270000000002       try = 280
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 81.93860000000001        try = 281
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 107.41300000000003       try = 282
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 106.75640000000003       try = 283
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 131.13540000000003       try = 284
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 107.39100000000003       try = 285
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 131.19200000000004       try = 286
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 130.11120000000003       try = 287
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 152.81679999999997       try = 288
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 59.04339999999999        try = 289
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 82.30120000000001        try = 290
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 81.64980000000001        try = 291
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 103.8122                 try = 292
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 82.44140000000002        try = 293
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 104.0258                 try = 294
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 102.95020000000001       try = 295
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 123.4392                 try = 296
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 81.85210000000001        try = 297
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 104.2853                 try = 298
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 103.73730000000002       try = 299
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 125.07510000000002       try = 300
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 103.71390000000002       try = 301
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 124.47370000000001       try = 302
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 123.50150000000004       try = 303
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 143.16590000000005       try = 304
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 82.0969                  try = 305
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 96.08330000000002        try = 306
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 95.86470000000003        try = 307
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 108.75569999999999       try = 308
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 96.85770000000001        try = 309
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 109.1707                 try = 310
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 108.5279                 try = 311
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 119.74549999999999       try = 312
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 95.83260000000003        try = 313
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 108.9944                 try = 314
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 108.87920000000001       try = 315
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 120.94560000000001       try = 316
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 109.05720000000001       try = 317
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 120.5456                 try = 318
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 120.0062                 try = 319
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 130.3992                 try = 320
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 60.5183                  try = 321
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 83.0549                  try = 322
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 82.24530000000001        try = 323
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 103.68650000000001       try = 324
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 83.39570000000002        try = 325
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 104.2589                 try = 326
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 103.0251                 try = 327
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 122.7929                 try = 328
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 82.53660000000002        try = 329
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 104.24860000000001       try = 330
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 103.54240000000001       try = 331
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 124.159                  try = 332
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 103.87780000000004       try = 333
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 123.91640000000001       try = 334
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 122.78600000000003       try = 335
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 141.7292                 try = 336
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 83.68839999999999        try = 337
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 96.95360000000001        try = 338
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 96.57680000000002        try = 339
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.7466                 try = 340
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 97.92860000000002        try = 341
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 109.5204                 try = 342
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.7194                 try = 343
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 119.21579999999999       try = 344
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 96.6337                  try = 345
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 109.07430000000001       try = 346
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.8009                 try = 347
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 120.1461                 try = 348
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 109.33770000000001       try = 349
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 120.1049                 try = 350
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 119.40730000000002       try = 351
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 129.0791                 try = 352
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 89.52150000000002        try = 353
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 99.7455                  try = 354
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 99.47730000000001        try = 355
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.60590000000002       try = 356
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 100.17110000000001       try = 357
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.72170000000001       try = 358
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.0293                 try = 359
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 115.48450000000003       try = 360
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 99.35940000000002        try = 361
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.75880000000002       try = 362
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.59400000000002       try = 363
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 116.89800000000004       try = 364
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.47280000000002       try = 365
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 116.19880000000002       try = 366
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 115.60980000000005       try = 367
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 122.24040000000002       try = 368
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 107.32140000000001       try = 369
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.27400000000002       try = 370
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.43860000000002       try = 371
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.29580000000001       try = 372
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 109.33380000000002       try = 373
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.613                  try = 374
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.35340000000002       try = 375
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 106.53719999999998       try = 376
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.08630000000002       try = 377
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.21430000000001       try = 378
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.48230000000001       try = 379
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 107.5149                 try = 380
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.56250000000001       try = 381
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 107.01709999999999       try = 382
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 106.8609                 try = 383
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 104.2201                 try = 384
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 53.484700000000004       try = 385
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 78.43430000000002        try = 386
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 77.68390000000002        try = 387
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 101.53810000000001       try = 388
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 78.73750000000003        try = 389
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 102.01370000000001       try = 390
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 100.83910000000003       try = 391
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 123.01990000000002       try = 392
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 77.96480000000003        try = 393
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 102.08980000000001       try = 394
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 101.44280000000002       try = 395
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 124.47240000000001       try = 396
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 101.68140000000002       try = 397
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 124.13300000000002       try = 398
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 123.06180000000003       try = 399
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 144.41799999999998       try = 400
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 78.28080000000001        try = 401
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 93.95900000000002        try = 402
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 93.64140000000002        try = 403
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 108.22420000000001       try = 404
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 94.89640000000001        try = 405
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 108.90120000000002       try = 406
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 108.15940000000002       try = 407
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 121.06880000000001       try = 408
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 93.68790000000001        try = 409
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 108.54150000000001       try = 410
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 108.32730000000001       try = 411
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 122.08550000000001       try = 412
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 108.76730000000002       try = 413
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 121.94750000000002       try = 414
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 121.30910000000003       try = 415
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 133.3939                 try = 416
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 82.68430000000001        try = 417
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 95.3213                  try = 418
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 95.1123                  try = 419
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 106.65390000000001       try = 420
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 95.70930000000003        try = 421
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 106.6729                 try = 422
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 106.03970000000002       try = 423
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 115.90790000000001       try = 424
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 94.98400000000001        try = 425
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 106.7964                 try = 426
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 106.69080000000001       try = 427
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 117.4078                 try = 428
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 106.47280000000002       try = 429
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 116.6118                 try = 430
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 116.08200000000002       try = 431
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 125.1256                 try = 432
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 102.1102                 try = 433
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 105.47580000000002       try = 434
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 105.69960000000002       try = 435
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 107.96979999999999       try = 436
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 106.49800000000002       try = 437
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 108.19019999999999       try = 438
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 107.9898                 try = 439
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 108.58659999999999       try = 440
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 105.33690000000003       try = 441
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 107.87790000000001       try = 442
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 108.2051                 try = 443
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 109.65069999999999       try = 444
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 108.1885                 try = 445
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 109.0561                 try = 446
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 108.95909999999999       try = 447
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 108.73129999999999       try = 448
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 83.81960000000002        try = 449
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 95.73540000000001        try = 450
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 95.36820000000003        try = 451
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 106.18860000000002       try = 452
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 96.32400000000003        try = 453
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 106.56640000000002       try = 454
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 105.77500000000002       try = 455
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 114.922                  try = 456
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 95.32890000000002        try = 457
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 106.42010000000002       try = 458
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 106.15630000000002       try = 459
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 116.1521                 try = 460
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 106.29710000000003       try = 461
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 115.71490000000003       try = 462
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 115.02690000000003       try = 463
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 123.34930000000001       try = 464
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 103.36210000000001       try = 465
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 106.00650000000002       try = 466
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 106.07210000000002       try = 467
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.62110000000001       try = 468
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.22930000000002       try = 469
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 108.20030000000001       try = 470
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.8417                 try = 471
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.71730000000001       try = 472
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 105.79840000000002       try = 473
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.6182                 try = 474
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.7872                 try = 475
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 108.5116                 try = 476
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 108.1294                 try = 477
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 108.27580000000002       try = 478
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 108.0206                 try = 479
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.07159999999999       try = 480
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 110.57780000000001       try = 481
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 110.18100000000001       try = 482
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 110.35520000000001       try = 483
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.863                  try = 484
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 110.85440000000003       try = 485
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.78420000000001       try = 486
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.5342                 try = 487
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 105.3686                 try = 488
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 109.90670000000001       try = 489
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.68530000000001       try = 490
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.9629                 try = 491
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 106.6461                 try = 492
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.64710000000002       try = 493
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 105.75230000000002       try = 494
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 105.60570000000001       try = 495
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 101.61550000000001       try = 496
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 124.7501                 try = 497
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 115.0819                 try = 498
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 115.68889999999999       try = 499
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 104.92530000000001       try = 500
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 116.38950000000001       try = 501
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 105.0479                 try = 502
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 105.2307                 try = 503
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 92.7937                  try = 504
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 115.00600000000001       try = 505
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 104.51320000000001       try = 506
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 105.2236                 try = 507
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 93.6354                  try = 508
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 105.10920000000002       try = 509
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 92.94300000000001        try = 510
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 93.2292                  try = 511
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 79.9676                  try = 512
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 30.5407                  try = 513
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 63.26869999999999        try = 514
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 62.08849999999999        try = 515
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 93.72109999999996        try = 516
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 63.05629999999999        try = 517
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 94.11089999999997        try = 518
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 92.50649999999997        try = 519
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 122.46569999999998       try = 520
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 62.61659999999999        try = 521
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 94.52                    try = 522
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 93.44319999999999        try = 523
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 124.25119999999998       try = 524
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 93.596                   try = 525
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 123.82600000000001       try = 526
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 122.325                  try = 527
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 151.45960000000002       try = 528
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 56.62259999999999        try = 529
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 80.07919999999999        try = 530
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 79.33179999999999        try = 531
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 101.693                  try = 532
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 80.50099999999998        try = 533
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 102.2842                 try = 534
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 101.1126                 try = 535
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 121.80039999999998       try = 536
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 79.62549999999997        try = 537
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 102.25750000000001       try = 538
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 101.6135                 try = 539
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 123.15010000000001       try = 540
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 101.96770000000001       try = 541
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 122.92630000000001       try = 542
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 121.85810000000001       try = 543
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 141.72129999999999       try = 544
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 64.80229999999999        try = 545
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 85.21769999999998        try = 546
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 84.57889999999998        try = 547
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 103.89889999999997       try = 548
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 85.09009999999999        try = 549
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 103.83209999999998       try = 550
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 102.7691                 try = 551
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 120.41569999999997       try = 552
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 84.69779999999999        try = 553
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 104.28859999999999       try = 554
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 103.75319999999999       try = 555
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 122.24860000000001       try = 556
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 103.4494                 try = 557
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 121.36680000000001       try = 558
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 120.40720000000002       try = 559
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 137.2292                 try = 560
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 85.51399999999998        try = 561
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 96.65799999999999        try = 562
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 96.452                   try = 563
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 106.50059999999999       try = 564
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 97.1646                  try = 565
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 106.63519999999998       try = 566
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 106.005                  try = 567
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 114.38019999999999       try = 568
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 96.3365                  try = 569
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 106.6559                 try = 570
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 106.5533                 try = 571
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 115.7773                 try = 572
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 106.4509                 try = 573
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 115.0969                 try = 574
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 114.57010000000002       try = 575
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 122.12070000000003       try = 576
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 66.80399999999999        try = 577
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 86.49819999999998        try = 578
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 85.70119999999997        try = 579
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 104.29999999999997       try = 580
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 86.57119999999999        try = 581
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 104.59199999999998       try = 582
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 103.3708                 try = 583
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 120.29619999999998       try = 584
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 85.9091                  try = 585
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 104.7787                 try = 586
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 104.0851                 try = 587
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 121.8593                 try = 588
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 104.1401                 try = 589
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 121.3363                 try = 590
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 120.2185                 try = 591
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 136.3193                 try = 592
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 87.63229999999999        try = 593
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 98.0551                  try = 594
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 97.6909                  try = 595
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 107.01829999999998       try = 596
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 98.76230000000001        try = 597
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 107.5117                 try = 598
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 106.7233                 try = 599
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 114.3773                 try = 600
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 97.66439999999999        try = 601
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 107.2626                 try = 602
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 107.0018                 try = 603
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 115.50460000000001       try = 604
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 107.2582                 try = 605
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 115.18300000000002       try = 606
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 114.49800000000002       try = 607
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 121.32740000000003       try = 608
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 98.62419999999999        try = 609
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 106.0058                 try = 610
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 105.75019999999999       try = 611
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 112.03640000000001       try = 612
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 106.1636                 try = 613
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 111.87180000000001       try = 614
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 111.192                  try = 615
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 115.8048                 try = 616
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 105.54890000000002       try = 617
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 112.10590000000002       try = 618
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 111.95370000000001       try = 619
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 117.41530000000002       try = 620
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 111.5521                 try = 621
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 116.43570000000001       try = 622
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 115.85930000000003       try = 623
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 119.64750000000002       try = 624
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 114.08230000000002       try = 625
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 112.1925                 try = 626
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 112.36970000000001       try = 627
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 109.3845                 try = 628
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 112.9845                 try = 629
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 109.4213                 try = 630
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 109.1743                 try = 631
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 104.5157                 try = 632
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 111.93400000000003       try = 633
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 109.21960000000001       try = 634
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 109.50019999999999       try = 635
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 105.69040000000001       try = 636
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 109.30000000000001       try = 637
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 104.9122                 try = 638
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 104.7686                 try = 639
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 99.28540000000002        try = 640
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 58.71359999999999        try = 641
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 80.82079999999998        try = 642
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 80.08299999999998        try = 643
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 101.09479999999999       try = 644
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 80.85619999999999        try = 645
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 101.29                   try = 646
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 100.12799999999997       try = 647
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 119.4664                 try = 648
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 80.28049999999999        try = 649
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 101.56309999999999       try = 650
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 100.92869999999998       try = 651
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 121.11589999999998       try = 652
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 100.8869                 try = 653
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 120.49610000000001       try = 654
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 119.4375                 try = 655
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 137.95130000000003       try = 656
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 81.16789999999997        try = 657
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 94.00369999999998        try = 658
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 93.6987                  try = 659
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 105.43909999999998       try = 660
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 94.6733                  try = 661
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 105.8357                 try = 662
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 105.10650000000001       try = 663
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 115.1735                 try = 664
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 93.6618                  try = 665
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 105.673                  try = 666
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 105.4714                 try = 667
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 116.38720000000002       try = 668
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 105.63100000000001       try = 669
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 115.96880000000003       try = 670
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 115.34300000000003       try = 671
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 124.5854                 try = 672
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 90.73019999999998        try = 673
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 100.52479999999997       try = 674
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 100.32839999999999       try = 675
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 109.02759999999999       try = 676
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 100.645                  try = 677
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 108.7662                 try = 678
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 108.1456                 try = 679
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 115.17139999999999       try = 680
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 100.1167                 try = 681
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 109.0867                 try = 682
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 108.99369999999999       try = 683
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 116.86829999999999       try = 684
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 108.4953                 try = 685
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 115.7919                 try = 686
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 115.27470000000001       try = 687
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 121.47590000000001       try = 688
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 107.81429999999997       try = 689
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 108.33749999999999       try = 690
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 108.5739                 try = 691
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 108.00169999999997       try = 692
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 109.09190000000001       try = 693
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 107.94169999999998       try = 694
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 107.7539                 try = 695
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 105.50829999999999       try = 696
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 108.12780000000002       try = 697
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 107.82639999999999       try = 698
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 108.16619999999998       try = 699
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 106.76939999999999       try = 700
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 107.8692                 try = 701
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 105.89439999999999       try = 702
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 105.81                   try = 703
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 102.7398                 try = 704
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 92.39229999999999        try = 705
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 101.46569999999998       try = 706
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 101.11110000000001       try = 707
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 109.08909999999997       try = 708
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 101.78649999999999       try = 709
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 109.18650000000001       try = 710
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 108.40769999999999       try = 711
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 114.7123                 try = 712
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 100.9884                 try = 713
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 109.2372                 try = 714
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 108.98599999999999       try = 715
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 116.13940000000002       try = 716
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 108.84640000000002       try = 717
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 115.42180000000003       try = 718
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 114.74640000000001       try = 719
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 120.22640000000001       try = 720
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.593                  try = 721
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.39499999999998       try = 722
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.47319999999999       try = 723
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.17979999999999       try = 724
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.35000000000001       try = 725
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.4786                 try = 726
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.1326                 try = 727
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 105.1658                 try = 728
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.1161                 try = 729
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.0935                 try = 730
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.2751                 try = 731
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 106.1571                 try = 732
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.33690000000001       try = 733
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 105.64090000000002       try = 734
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 105.39830000000003       try = 735
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 101.60690000000002       try = 736
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 121.96750000000002       try = 737
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 118.72830000000002       try = 738
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 118.9151                 try = 739
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 114.58049999999999       try = 740
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 119.13390000000003       try = 741
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 114.22130000000001       try = 742
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 113.9839                 try = 743
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 107.97590000000001       try = 744
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 118.3832                 try = 745
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 114.3194                 try = 746
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 114.6096                 try = 747
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 109.4504                 try = 748
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 114.0134                 try = 749
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 108.27620000000002       try = 750
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 108.14220000000003       try = 751
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 101.30960000000002       try = 752
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 133.79800000000003       try = 753
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 121.2874                 try = 754
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 121.907                  try = 755
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.30099999999999       try = 756
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 122.32720000000003       try = 757
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.14320000000002       try = 758
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.3386                 try = 759
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 93.0592                  try = 760
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 121.14070000000001       try = 761
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 107.80550000000002       try = 762
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.5285                 try = 763
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 94.0979                  try = 764
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.13370000000002       try = 765
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 93.12510000000002        try = 766
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 93.42390000000002        try = 767
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 77.31989999999999        try = 768
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 54.595499999999994       try = 769
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 79.04829999999997        try = 770
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 78.22869999999998        try = 771
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 101.58609999999997       try = 772
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 79.38069999999998        try = 773
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 102.16009999999999       try = 774
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 100.91629999999999       try = 775
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 122.60029999999998       try = 776
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 78.53019999999998        try = 777
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 102.15839999999999       try = 778
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 101.4422                 try = 779
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 123.975                  try = 780
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 101.7792                 try = 781
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 123.73400000000001       try = 782
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 122.59360000000002       try = 783
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 143.45300000000006       try = 784
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 79.11539999999998        try = 785
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 94.29679999999999        try = 786
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 93.90999999999998        try = 787
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 107.99599999999998       try = 788
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 95.26339999999999        try = 789
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.7714                 try = 790
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 107.96039999999999       try = 791
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 120.37299999999998       try = 792
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 93.9771                  try = 793
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.3339                 try = 794
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.0505                 try = 795
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 121.31190000000001       try = 796
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.58890000000001       try = 797
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 121.27230000000002       try = 798
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 120.56470000000002       try = 799
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 132.15270000000004       try = 800
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 83.55809999999997        try = 801
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 95.69829999999999        try = 802
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 95.42009999999999        try = 803
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 106.46489999999997       try = 804
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 96.11549999999998        try = 805
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 106.58229999999999       try = 806
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 105.87989999999999       try = 807
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 115.25129999999997       try = 808
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 95.3124                  try = 809
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 106.628                  try = 810
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 106.4532                 try = 811
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 116.67339999999999       try = 812
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 106.3336                 try = 813
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 115.9758                 try = 814
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 115.3768                 try = 815
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 123.92360000000001       try = 816
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 102.70779999999999       try = 817
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 105.5766                 try = 818
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 105.7312                 try = 819
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.50459999999997       try = 820
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 106.628                  try = 821
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.82339999999998       try = 822
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.55379999999998       try = 823
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.65379999999998       try = 824
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 105.38910000000001       try = 825
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.43329999999999       try = 826
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.6913                 try = 827
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 108.64009999999999       try = 828
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.7731                 try = 829
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 108.14389999999997       try = 830
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.9777                 try = 831
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 107.2531                 try = 832
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 85.58619999999998        try = 833
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 97.00519999999999        try = 834
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 96.56879999999998        try = 835
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 106.89239999999998       try = 836
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 97.62299999999999        try = 837
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 107.36859999999999       try = 838
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 106.508                  try = 839
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 115.15819999999997       try = 840
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 96.5501                  try = 841
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 107.1445                 try = 842
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 106.8115                 try = 843
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 116.31049999999999       try = 844
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 107.0507                 try = 845
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 115.97170000000001       try = 846
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 115.2145                 try = 847
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 123.0401                 try = 848
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 104.85249999999999       try = 849
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 107.00009999999999       try = 850
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 106.9965                 try = 851
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.04869999999997       try = 852
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.2521                 try = 853
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.72629999999998       try = 854
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.29849999999998       try = 855
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 107.67729999999997       try = 856
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 106.74340000000001       try = 857
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.06639999999999       try = 858
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.16619999999999       try = 859
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.39379999999998       try = 860
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.60679999999999       try = 861
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.25639999999999       try = 862
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 107.932                  try = 863
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 106.4862                 try = 864
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 112.10739999999998       try = 865
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.21379999999999       try = 866
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.3188                 try = 867
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 109.32979999999998       try = 868
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.9164                 try = 869
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 109.34939999999999       try = 870
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 109.03019999999998       try = 871
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 105.36779999999999       try = 872
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 110.8909                 try = 873
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 109.17269999999999       try = 874
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 109.3811                 try = 875
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 106.5675                 try = 876
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 109.1637                 try = 877
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 105.77210000000001       try = 878
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 105.55630000000001       try = 879
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 101.0693                 try = 880
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 126.00349999999999       try = 881
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 115.83849999999998       try = 882
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 116.37629999999999       try = 883
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 105.11589999999998       try = 884
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 117.17530000000001       try = 885
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 105.33689999999999       try = 886
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 105.45049999999998       try = 887
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 92.51669999999997        try = 888
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 115.714                  try = 889
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 104.7244                 try = 890
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 105.3656                 try = 891
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 93.28059999999999        try = 892
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 105.3496                 try = 893
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 92.6866                  try = 894
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 92.9036                  try = 895
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 79.14519999999999        try = 896
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 79.54339999999998        try = 897
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 93.37539999999998        try = 898
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 92.99819999999998        try = 899
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 105.73479999999998       try = 900
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 93.95559999999999        try = 901
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 106.1142                 try = 902
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 105.3128                 try = 903
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 116.37599999999999       try = 904
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 92.9691                  try = 905
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 105.9765                 try = 906
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 105.70270000000001       try = 907
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 117.6147                 try = 908
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 105.84510000000002       try = 909
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 117.17910000000002       try = 910
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 116.48110000000001       try = 911
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 126.7197                 try = 912
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 100.4357                 try = 913
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 104.9963                 try = 914
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 105.05190000000002       try = 915
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 108.51709999999999       try = 916
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 106.2107                 try = 917
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 109.0979                 try = 918
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 108.7293                 try = 919
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 110.52109999999999       try = 920
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 104.78840000000002       try = 921
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 108.5244                 try = 922
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 108.68339999999999       try = 923
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 111.324                  try = 924
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 109.02720000000002       try = 925
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 111.08980000000001       try = 926
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 110.82460000000002       try = 927
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 111.79180000000001       try = 928
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 106.261                  try = 929
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 107.78039999999999       try = 930
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 107.9446                 try = 931
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.36859999999999       try = 932
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.4454                 try = 933
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.29139999999998       try = 934
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.03139999999998       try = 935
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 106.782                  try = 936
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 107.50630000000001       try = 937
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.20109999999998       try = 938
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.46869999999998       try = 939
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.06809999999999       try = 940
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 108.1545                 try = 941
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 107.1759                 try = 942
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 107.0193                 try = 943
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 104.94529999999999       try = 944
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 121.78309999999999       try = 945
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 114.03109999999998       try = 946
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 114.62809999999998       try = 947
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 105.78069999999998       try = 948
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 115.33030000000001       try = 949
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 105.90490000000001       try = 950
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 106.07770000000002       try = 951
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 95.55689999999998        try = 952
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 113.95540000000001       try = 953
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 105.3788                 try = 954
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 106.0792                 try = 955
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 96.40719999999997        try = 956
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 105.96640000000001       try = 957
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 95.7164                  try = 958
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 95.9926                  try = 959
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 84.64719999999998        try = 960
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 107.9495                 try = 961
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.7477                 try = 962
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.75370000000001       try = 963
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.4565                 try = 964
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 109.61330000000001       try = 965
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.7381                 try = 966
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.3199                 try = 967
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 106.34929999999999       try = 968
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.40440000000002       try = 969
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.37800000000001       try = 970
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.48740000000001       try = 971
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 107.36559999999999       try = 972
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.53200000000002       try = 973
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 106.83220000000001       try = 974
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 106.51740000000001       try = 975
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 103.7222                 try = 976
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 123.5882                 try = 977
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 115.11499999999998       try = 978
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 115.55379999999998       try = 979
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 105.98519999999998       try = 980
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 116.61480000000002       try = 981
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 106.46819999999998       try = 982
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 106.4828                 try = 983
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 95.24079999999998        try = 984
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 114.97010000000002       try = 985
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 105.67229999999999       try = 986
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 106.2145                 try = 987
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 95.82129999999998        try = 988
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 106.46050000000001       try = 989
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 95.48930000000001        try = 990
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 95.60730000000001        try = 991
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 83.5407                  try = 992
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 132.22570000000002       try = 993
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 120.71130000000001       try = 994
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 121.2587                 try = 995
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.6489                 try = 996
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 121.6617                 try = 997
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.47389999999999       try = 998
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.5971                 try = 999
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 94.31389999999998        try = 1000
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 120.5002                 try = 1001
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.16120000000001       try = 1002
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.812                  try = 1003
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 95.37759999999999        try = 1004
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.40000000000002       try = 1005
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 94.3876                  try = 1006
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 94.6142                  try = 1007
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 79.50639999999999        try = 1008
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 142.4942                 try = 1009
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 121.70840000000001       try = 1010
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 122.6886                 try = 1011
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 100.80739999999996       try = 1012
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 123.29300000000002       try = 1013
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 100.83379999999998       try = 1014
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 101.38979999999998       try = 1015
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 77.83519999999999        try = 1016
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 121.69570000000002       try = 1017
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 100.08529999999999       try = 1018
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 101.1689                 try = 1019
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 78.4631                  try = 1020
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 100.95830000000001       try = 1021
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 77.67449999999998        try = 1022
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 78.3339                  try = 1023
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 53.954699999999995       try = 1024
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 27.920099999999998       try = 1025
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 61.60309999999999        try = 1026
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 60.51689999999999        try = 1027
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 93.10450000000002        try = 1028
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 61.4661                  try = 1029
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 93.4757                  try = 1030
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 91.96530000000001        try = 1031
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 122.87950000000001       try = 1032
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 61.0244                  try = 1033
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 93.8828                  try = 1034
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 92.9                     try = 1035
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 124.66300000000001       try = 1036
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 93.03420000000001        try = 1037
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 124.2192                 try = 1038
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 122.81220000000002       try = 1039
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 152.90179999999998       try = 1040
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 55.76099999999999        try = 1041
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 80.1726                  try = 1042
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 79.51920000000001        try = 1043
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 102.8354                 try = 1044
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 80.66980000000001        try = 1045
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 103.40800000000003       try = 1046
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 102.33040000000003       try = 1047
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 123.9732                 try = 1048
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 79.7923                  try = 1049
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 103.37930000000003       try = 1050
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 102.82930000000002       try = 1051
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 125.3209                 try = 1052
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 103.16490000000002       try = 1053
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 125.07850000000002       try = 1054
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 124.10430000000001       try = 1055
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 144.92249999999996       try = 1056
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 61.35309999999999        try = 1057
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 82.72350000000003        try = 1058
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 82.17870000000003        try = 1059
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 102.45370000000001       try = 1060
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 82.67130000000003        try = 1061
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 102.36830000000002       try = 1062
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 101.39930000000001       try = 1063
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 120.0009                 try = 1064
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 82.27700000000003        try = 1065
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 102.82280000000002       try = 1066
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 102.38140000000001       try = 1067
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 121.83180000000002       try = 1068
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 102.05900000000001       try = 1069
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 120.93140000000001       try = 1070
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 120.06580000000001       try = 1071
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 137.84279999999995       try = 1072
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 83.82380000000002        try = 1073
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 95.92280000000002        try = 1074
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 95.81080000000003        try = 1075
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 106.81440000000002       try = 1076
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 96.50480000000002        try = 1077
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 106.93040000000002       try = 1078
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 106.39420000000001       try = 1079
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 115.72440000000002       try = 1080
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 95.67470000000002        try = 1081
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 106.94910000000002       try = 1082
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 106.94050000000001       try = 1083
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 117.11950000000002       try = 1084
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 106.8195                 try = 1085
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 116.42049999999999       try = 1086
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 115.98770000000002       try = 1087
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 124.4933                 try = 1088
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 62.67699999999999        try = 1089
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 83.3262                  try = 1090
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 82.62320000000001        try = 1091
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 102.17699999999999       try = 1092
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 83.47460000000001        try = 1093
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 102.4504                 try = 1094
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 101.3232                 try = 1095
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 119.20359999999998       try = 1096
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 82.81050000000002        try = 1097
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 102.63510000000001       try = 1098
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 102.0355                 try = 1099
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 120.76469999999999       try = 1100
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 102.07190000000001       try = 1101
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 120.2231                 try = 1102
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 119.19929999999998       try = 1103
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 136.25509999999994       try = 1104
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 85.2643                  try = 1105
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 96.64210000000003        try = 1106
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 96.37190000000001        try = 1107
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 106.65430000000002       try = 1108
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 97.4247                  try = 1109
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 107.12910000000001       try = 1110
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 106.43469999999999       try = 1111
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 115.0437                 try = 1112
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 96.3248                  try = 1113
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 106.87800000000001       try = 1114
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 106.71120000000002       try = 1115
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 116.169                  try = 1116
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 106.94900000000001       try = 1117
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 115.82879999999999       try = 1118
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 115.23780000000002       try = 1119
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 123.02219999999998       try = 1120
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 93.66860000000001        try = 1121
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 102.00520000000003       try = 1122
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 101.84360000000002       try = 1123
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 109.08480000000003       try = 1124
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 102.23840000000003       try = 1125
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 108.90160000000003       try = 1126
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 108.31580000000002       try = 1127
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 113.88360000000003       try = 1128
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 101.62170000000003       try = 1129
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 109.13370000000003       try = 1130
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 109.07550000000003       try = 1131
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 115.49210000000004       try = 1132
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 108.65530000000001       try = 1133
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 114.49390000000002       try = 1134
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 114.01150000000004       try = 1135
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 118.75470000000003       try = 1136
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 110.88570000000003       try = 1137
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 109.95090000000002       try = 1138
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 110.22210000000003       try = 1139
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.19190000000003       try = 1140
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 110.81830000000004       try = 1141
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.21010000000001       try = 1142
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.0571                 try = 1143
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 104.35350000000001       try = 1144
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 109.76580000000003       try = 1145
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.00640000000001       try = 1146
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.38100000000001       try = 1147
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 105.52620000000002       try = 1148
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.1622                 try = 1149
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 104.7294                 try = 1150
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 104.67980000000001       try = 1151
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 100.15160000000002       try = 1152
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 55.264599999999994       try = 1153
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 78.3268                  try = 1154
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 77.683                   try = 1155
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 99.6498                  try = 1156
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 78.4376                  try = 1157
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 99.8264                  try = 1158
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 98.7584                  try = 1159
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 119.05179999999999       try = 1160
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 77.85990000000001        try = 1161
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 100.0975                 try = 1162
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 99.5571                  try = 1163
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 120.6993                 try = 1164
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 99.49670000000002        try = 1165
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 120.0609                 try = 1166
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 119.0963                 try = 1167
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 138.5651                 try = 1168
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 79.4779                  try = 1169
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 93.26870000000001        try = 1170
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 93.05770000000001        try = 1171
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 105.75310000000002       try = 1172
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 94.0137                  try = 1173
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 106.1311                 try = 1174
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 105.4959                 try = 1175
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 116.5179                 try = 1176
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 93.00019999999999        try = 1177
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 105.96640000000001       try = 1178
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 105.8588                 try = 1179
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 117.72959999999999       try = 1180
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 105.99980000000001       try = 1181
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 117.2926                 try = 1182
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 116.7608                 try = 1183
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 126.95819999999999       try = 1184
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 86.45260000000002        try = 1185
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 97.20220000000002        try = 1186
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 97.0998                  try = 1187
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 106.754                  try = 1188
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 97.3978                  try = 1189
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 106.474                  try = 1190
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 105.9474                 try = 1191
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 113.92819999999999       try = 1192
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 96.8675                  try = 1193
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 106.7925                 try = 1194
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 106.7935                 try = 1195
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 115.6231                 try = 1196
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 106.27650000000001       try = 1197
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 114.5281                 try = 1198
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 114.1049                 try = 1199
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 121.2611                 try = 1200
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 105.2957                 try = 1201
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 106.77390000000001       try = 1202
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.10430000000001       try = 1203
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.48710000000001       try = 1204
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.60370000000002       try = 1205
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.40849999999999       try = 1206
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.3147                 try = 1207
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 106.02409999999999       try = 1208
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 106.6376                 try = 1209
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.2912                 try = 1210
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.725                  try = 1211
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.2832                 try = 1212
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 107.40939999999999       try = 1213
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 106.38959999999999       try = 1214
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 106.3992                 try = 1215
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 104.28399999999999       try = 1216
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 87.43690000000002        try = 1217
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 97.4653                  try = 1218
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 97.20470000000002        try = 1219
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 106.13770000000001       try = 1220
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 97.86149999999999        try = 1221
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 106.21650000000001       try = 1222
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 105.53169999999999       try = 1223
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 112.79129999999999       try = 1224
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 97.0614                  try = 1225
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 106.26520000000001       try = 1226
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 106.10799999999999       try = 1227
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 114.2164                 try = 1228
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 105.94980000000001       try = 1229
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 113.48020000000001       try = 1230
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 112.8988                 try = 1231
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 119.3338                 try = 1232
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 106.39659999999999       try = 1233
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.1536                 try = 1234
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.3258                 try = 1235
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 106.9874                 try = 1236
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 108.18400000000001       try = 1237
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.2676                 try = 1238
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.01559999999999       try = 1239
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 105.0038                 try = 1240
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 106.9481                 try = 1241
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 106.8805                 try = 1242
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.15609999999998       try = 1243
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 105.9931                 try = 1244
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.1993                 try = 1245
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 105.4583                 try = 1246
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 105.30969999999999       try = 1247
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 102.4733                 try = 1248
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 116.18350000000001       try = 1249
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 113.89930000000001       try = 1250
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 114.18010000000001       try = 1251
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.8005                 try = 1252
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 114.3803                 try = 1253
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.42270000000002       try = 1254
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.2793                 try = 1255
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 105.22630000000001       try = 1256
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 113.6276                 try = 1257
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.51880000000001       try = 1258
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.903                  try = 1259
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 106.6988                 try = 1260
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.2882                 try = 1261
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 105.50600000000001       try = 1262
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 105.46600000000002       try = 1263
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 99.58840000000001        try = 1264
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 129.773                  try = 1265
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 118.2174                 try = 1266
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 118.93100000000001       try = 1267
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 106.28                   try = 1268
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 119.33260000000001       try = 1269
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 106.1036                 try = 1270
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 106.393                  try = 1271
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 92.0686                  try = 1272
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 118.14410000000001       try = 1273
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 105.7639                 try = 1274
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 106.5809                 try = 1275
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 93.1053                  try = 1276
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 106.1675                 try = 1277
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 92.11390000000002        try = 1278
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 92.50670000000001        try = 1279
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 77.3577                  try = 1280
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 53.20369999999999        try = 1281
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 78.6115                  try = 1282
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 77.8859                  try = 1283
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 102.19830000000002       try = 1284
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 79.01930000000002        try = 1285
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 102.75370000000002       try = 1286
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 101.60390000000002       try = 1287
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 124.24290000000002       try = 1288
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 78.16680000000001        try = 1289
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 102.75000000000003       try = 1290
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 102.12780000000002       try = 1291
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 125.61560000000003       try = 1292
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 102.44620000000003       try = 1293
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 125.35600000000004       try = 1294
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 124.30960000000002       try = 1295
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 146.12399999999997       try = 1296
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 79.4826                  try = 1297
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 95.61900000000003        try = 1298
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 95.32620000000003        try = 1299
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 110.36720000000001       try = 1300
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 96.66100000000002        try = 1301
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 111.12400000000002       try = 1302
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 110.40700000000002       try = 1303
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 123.7746                 try = 1304
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 95.37270000000001        try = 1305
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 110.68450000000003       try = 1306
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 110.49510000000002       try = 1307
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 124.7115                 try = 1308
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 111.01490000000003       try = 1309
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 124.65330000000003       try = 1310
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 124.03970000000002       try = 1311
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 136.5827                 try = 1312
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 81.33770000000001        try = 1313
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 94.43290000000003        try = 1314
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 94.24870000000003        try = 1315
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 106.24850000000004       try = 1316
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 94.92550000000001        try = 1317
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 106.34730000000003       try = 1318
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 105.73890000000004       try = 1319
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 116.06530000000001       try = 1320
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 94.12040000000003        try = 1321
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 106.39100000000003       try = 1322
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 106.31020000000004       try = 1323
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 117.48540000000003       try = 1324
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 106.17200000000004       try = 1325
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 116.76920000000001       try = 1326
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 116.26420000000003       try = 1327
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 125.766                  try = 1328
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 102.24640000000002       try = 1329
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 106.07020000000004       try = 1330
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 106.31880000000004       try = 1331
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 109.04720000000002       try = 1332
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 107.19700000000005       try = 1333
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 109.34740000000002       try = 1334
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 109.17180000000002       try = 1335
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 110.22680000000001       try = 1336
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 105.95610000000003       try = 1337
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 108.95530000000004       try = 1338
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 109.30730000000001       try = 1339
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 111.21110000000002       try = 1340
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 109.37050000000002       try = 1341
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 110.6963                 try = 1342
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 110.62410000000001       try = 1343
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 110.85450000000002       try = 1344
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 82.688                   try = 1345
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 95.06200000000003        try = 1346
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 94.71960000000001        try = 1347
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 105.99820000000001       try = 1348
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 95.75520000000002        try = 1349
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 106.45580000000001       try = 1350
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 105.68920000000001       try = 1351
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 115.2944                 try = 1352
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 94.68030000000002        try = 1353
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 106.22970000000002       try = 1354
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 105.99070000000002       try = 1355
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 116.4447                 try = 1356
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 106.21130000000002       try = 1357
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 116.0873                 try = 1358
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 115.42410000000001       try = 1359
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 124.2047                 try = 1360
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 103.7133                 try = 1361
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 106.81590000000001       try = 1362
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 106.90630000000002       try = 1363
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 108.9135                 try = 1364
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 108.14330000000001       try = 1365
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.5725                 try = 1366
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.2387                 try = 1367
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.57249999999999       try = 1368
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 106.63260000000001       try = 1369
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 108.9106                 try = 1370
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.1044                 try = 1371
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.287                  try = 1372
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.5264                 try = 1373
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.13099999999999       try = 1374
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.90060000000001       try = 1375
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.40979999999999       try = 1376
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.38060000000003       try = 1377
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.44200000000004       try = 1378
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.64100000000003       try = 1379
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 107.60700000000001       try = 1380
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 109.22000000000003       try = 1381
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 107.60800000000002       try = 1382
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 107.38280000000002       try = 1383
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 104.67540000000002       try = 1384
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.19250000000002       try = 1385
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 107.42930000000003       try = 1386
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 107.73170000000002       try = 1387
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 105.87310000000002       try = 1388
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 107.49570000000003       try = 1389
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 105.05910000000003       try = 1390
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 104.93730000000002       try = 1391
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 101.40530000000001       try = 1392
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 124.03570000000003       try = 1393
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 114.82570000000001       try = 1394
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 115.45750000000002       try = 1395
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 105.1521                 try = 1396
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 116.23790000000002       try = 1397
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 105.35450000000002       try = 1398
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 105.56210000000002       try = 1399
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 93.58330000000001        try = 1400
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 114.77460000000002       try = 1401
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 104.74000000000002       try = 1402
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 105.4752                 try = 1403
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 94.3452                  try = 1404
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 105.4406                 try = 1405
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 93.7326                  try = 1406
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 94.04360000000001        try = 1407
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 81.2402                  try = 1408
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 77.32320000000001        try = 1409
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 92.11020000000002        try = 1410
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 91.82700000000001        try = 1411
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 105.51860000000002       try = 1412
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 92.76580000000001        try = 1413
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 105.87940000000002       try = 1414
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 105.17200000000003       try = 1415
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 117.19020000000002       try = 1416
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 91.77730000000001        try = 1417
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 105.73970000000003       try = 1418
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 105.55990000000003       try = 1419
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 118.42689999999999       try = 1420
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 105.68370000000003       try = 1421
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 117.97270000000002       try = 1422
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 117.36870000000002       try = 1423
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 128.5623                 try = 1424
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 99.97450000000002        try = 1425
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 105.49010000000003       try = 1426
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 105.63970000000002       try = 1427
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 110.05990000000003       try = 1428
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 106.77990000000003       try = 1429
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 110.62210000000003       try = 1430
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 110.34750000000003       try = 1431
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 113.09430000000002       try = 1432
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 105.35560000000002       try = 1433
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 110.04660000000001       try = 1434
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 110.29960000000001       try = 1435
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 113.8952                 try = 1436
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 110.62480000000002       try = 1437
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 113.64240000000001       try = 1438
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 113.47120000000001       try = 1439
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 115.3934                 try = 1440
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 103.21220000000002       try = 1441
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 105.68660000000003       try = 1442
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 105.94480000000003       try = 1443
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.3238                 try = 1444
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 106.42700000000002       try = 1445
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.22800000000002       try = 1446
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.06200000000001       try = 1447
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 106.7676                 try = 1448
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 105.48590000000002       try = 1449
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.13570000000003       try = 1450
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.49730000000001       try = 1451
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 108.05170000000001       try = 1452
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.16450000000002       try = 1453
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.14090000000002       try = 1454
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.07830000000001       try = 1455
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 105.95930000000001       try = 1456
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 120.49330000000002       try = 1457
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 113.69630000000001       try = 1458
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 114.38730000000002       try = 1459
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 106.49490000000003       try = 1460
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 115.07090000000002       try = 1461
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 106.60050000000003       try = 1462
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 106.86730000000003       try = 1463
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 97.30149999999999        try = 1464
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 113.69400000000002       try = 1465
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 106.07240000000003       try = 1466
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 106.86680000000001       try = 1467
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 98.14979999999998        try = 1468
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 106.73540000000003       try = 1469
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 97.44040000000001        try = 1470
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 97.81060000000001        try = 1471
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 87.4202                  try = 1472
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 104.22290000000002       try = 1473
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 105.97610000000003       try = 1474
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.07610000000003       try = 1475
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.73390000000002       try = 1476
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.91710000000002       try = 1477
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.99690000000001       try = 1478
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.6727                 try = 1479
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 105.65709999999999       try = 1480
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 105.70620000000002       try = 1481
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.63480000000003       try = 1482
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.83820000000001       try = 1483
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.6714                 try = 1484
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.86420000000003       try = 1485
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 106.11940000000001       try = 1486
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 105.89860000000002       try = 1487
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 104.05839999999999       try = 1488
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 121.62060000000002       try = 1489
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 114.1024                 try = 1490
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 114.6352                 try = 1491
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 106.02160000000002       try = 1492
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 115.6776                 try = 1493
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 106.48600000000002       try = 1494
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 106.5946                 try = 1495
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 96.30759999999998        try = 1496
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 114.03090000000002       try = 1497
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 105.68810000000002       try = 1498
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 106.32430000000001       try = 1499
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 96.88609999999998        try = 1500
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 106.55170000000001       try = 1501
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 96.5355                  try = 1502
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 96.7475                  try = 1503
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 85.63589999999999        try = 1504
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 127.67050000000003       try = 1505
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 117.11110000000001       try = 1506
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 117.75250000000003       try = 1507
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 106.09770000000002       try = 1508
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 118.13690000000001       try = 1509
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 105.9041                 try = 1510
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 106.1213                 try = 1511
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 92.79310000000001        try = 1512
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 116.97340000000001       try = 1513
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 105.58940000000001       try = 1514
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 106.33420000000001       try = 1515
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 93.8548                  try = 1516
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 105.90360000000001       try = 1517
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 92.84620000000001        try = 1518
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 93.1668                  try = 1519
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 79.014                   try = 1520
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 139.69799999999998       try = 1521
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 119.86720000000001       try = 1522
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 120.94140000000002       try = 1523
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 100.01520000000001       try = 1524
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 121.52720000000001       try = 1525
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 100.023                  try = 1526
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 100.67299999999999       try = 1527
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 78.0734                  try = 1528
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 119.92790000000001       try = 1529
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 99.2725                  try = 1530
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 100.4501                 try = 1531
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 78.6993                  try = 1532
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 100.22090000000001       try = 1533
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 77.89210000000001        try = 1534
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 78.6455                  try = 1535
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 55.22129999999999        try = 1536
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 56.38239999999999        try = 1537
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 78.94780000000002        try = 1538
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 78.2348                  try = 1539
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 99.70479999999999        try = 1540
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 79.08780000000002        try = 1541
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 99.97980000000001        try = 1542
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 98.8426                  try = 1543
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 118.63919999999999       try = 1544
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 78.43230000000001        try = 1545
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 100.17310000000002       try = 1546
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 99.5635                  try = 1547
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 120.2089                 try = 1548
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 99.60150000000003        try = 1549
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 119.66890000000002       try = 1550
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 118.63510000000001       try = 1551
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 137.60709999999997       try = 1552
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 80.3195                  try = 1553
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 93.61350000000002        try = 1554
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 93.33330000000001        try = 1555
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 105.53190000000001       try = 1556
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 94.3877                  try = 1557
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 106.00830000000003       try = 1558
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 105.30390000000003       try = 1559
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 115.82910000000001       try = 1560
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 93.2964                  try = 1561
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 105.76580000000003       try = 1562
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 105.58900000000003       try = 1563
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 116.96300000000002       try = 1564
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 105.82840000000003       try = 1565
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 116.62440000000002       try = 1566
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 116.02340000000004       try = 1567
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 125.72399999999999       try = 1568
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 87.33340000000003        try = 1569
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 97.58620000000002        try = 1570
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 97.41460000000002        try = 1571
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 106.57200000000002       try = 1572
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 97.811                   try = 1573
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 106.39040000000003       try = 1574
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 105.79460000000003       try = 1575
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 113.27860000000001       try = 1576
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 97.20290000000001        try = 1577
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 106.63110000000003       try = 1578
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 106.56290000000003       try = 1579
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 114.89570000000003       try = 1580
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 106.14430000000003       try = 1581
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 113.89910000000003       try = 1582
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 113.40670000000003       try = 1583
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 120.0661                 try = 1584
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 105.90030000000003       try = 1585
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 106.88170000000004       try = 1586
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 107.14290000000003       try = 1587
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 107.02890000000001       try = 1588
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 107.74070000000003       try = 1589
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 107.04870000000003       try = 1590
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 106.88570000000003       try = 1591
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 105.09830000000001       try = 1592
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 106.69680000000004       try = 1593
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 106.85360000000003       try = 1594
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 107.21820000000001       try = 1595
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 106.27960000000002       try = 1596
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 107.00100000000002       try = 1597
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 105.48440000000002       try = 1598
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 105.42480000000003       try = 1599
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 102.81280000000004       try = 1600
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 89.21050000000002        try = 1601
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 98.74210000000001        try = 1602
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 98.4123                  try = 1603
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 106.8485                 try = 1604
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 99.1675                  try = 1605
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 107.02570000000001       try = 1606
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 106.27170000000001       try = 1607
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 113.0345                 try = 1608
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 98.28960000000001        try = 1609
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 106.99660000000002       try = 1610
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 106.7702                 try = 1611
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 114.38180000000001       try = 1612
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 106.71040000000002       try = 1613
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 113.74400000000003       try = 1614
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 113.09340000000003       try = 1615
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 119.03159999999998       try = 1616
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.894                  try = 1617
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 108.15420000000002       try = 1618
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 108.25720000000001       try = 1619
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.422                  try = 1620
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 109.21380000000002       try = 1621
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.8006                 try = 1622
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.47940000000001       try = 1623
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 104.97080000000001       try = 1624
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.90010000000002       try = 1625
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.33570000000002       try = 1626
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.54209999999999       try = 1627
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 105.88230000000001       try = 1628
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.68370000000002       try = 1629
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 105.44590000000002       try = 1630
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 105.22810000000003       try = 1631
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 101.89490000000002       try = 1632
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 117.72010000000002       try = 1633
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 114.93910000000002       try = 1634
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 115.15070000000003       try = 1635
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 111.27430000000003       try = 1636
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 115.44930000000002       try = 1637
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 110.99490000000003       try = 1638
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 110.78230000000002       try = 1639
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 105.23250000000003       try = 1640
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 114.61880000000002       try = 1641
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 111.01320000000003       try = 1642
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 111.32820000000002       try = 1643
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 106.62720000000003       try = 1644
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 110.81180000000002       try = 1645
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 105.53280000000002       try = 1646
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 105.42360000000002       try = 1647
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 99.04920000000003        try = 1648
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 131.0334                 try = 1649
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 118.98100000000002       try = 1650
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 119.62540000000003       try = 1651
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 106.47760000000002       try = 1652
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 120.12540000000004       try = 1653
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 106.39960000000002       try = 1654
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 106.61980000000003       try = 1655
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 91.79860000000002        try = 1656
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 118.85910000000004       try = 1657
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 105.98210000000003       try = 1658
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 106.72990000000003       try = 1659
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 92.75750000000002        try = 1660
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 106.41490000000003       try = 1661
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 91.86450000000004        try = 1662
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 92.18810000000002        try = 1663
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 76.54230000000003        try = 1664
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 82.78890000000001        try = 1665
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 94.7335                  try = 1666
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 94.4629                  try = 1667
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 105.31210000000002       try = 1668
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 95.1213                  try = 1669
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 105.39250000000001       try = 1670
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 104.69770000000001       try = 1671
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 113.8735                 try = 1672
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 94.3298                  try = 1673
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 105.44980000000001       try = 1674
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 105.2826                 try = 1675
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 115.3072                 try = 1676
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 105.12600000000002       try = 1677
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 114.57260000000004       try = 1678
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 113.98120000000003       try = 1679
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 122.3324                 try = 1680
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 103.09840000000001       try = 1681
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 105.77160000000002       try = 1682
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 105.93380000000002       try = 1683
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.51159999999999       try = 1684
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 106.79360000000001       try = 1685
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.7934                 try = 1686
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.5314                 try = 1687
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.43580000000003       try = 1688
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 105.56630000000003       try = 1689
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.41490000000002       try = 1690
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.68050000000001       try = 1691
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 108.43370000000002       try = 1692
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.72530000000002       try = 1693
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.90050000000004       try = 1694
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.74190000000003       try = 1695
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 106.82170000000002       try = 1696
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 111.49490000000002       try = 1697
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 111.12690000000002       try = 1698
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 111.39770000000001       try = 1699
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.93430000000001       try = 1700
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 111.59950000000002       try = 1701
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.55810000000001       try = 1702
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.4047                 try = 1703
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 106.2679                 try = 1704
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 110.85540000000002       try = 1705
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.6628                 try = 1706
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 110.037                  try = 1707
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 107.749                  try = 1708
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.42380000000001       try = 1709
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 106.55780000000003       try = 1710
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 106.50780000000002       try = 1711
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 102.54640000000002       try = 1712
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 126.43420000000003       try = 1713
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 116.79480000000002       try = 1714
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 117.49840000000002       try = 1715
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 106.76360000000003       try = 1716
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 117.90160000000003       try = 1717
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 106.58880000000003       try = 1718
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 106.86820000000002       try = 1719
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 94.46000000000001        try = 1720
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 116.72170000000003       try = 1721
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 106.25770000000003       try = 1722
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 107.06470000000002       try = 1723
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 95.5053                  try = 1724
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 106.65290000000003       try = 1725
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 94.51550000000002        try = 1726
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 94.89830000000002        try = 1727
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 81.66550000000001        try = 1728
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 113.03240000000002       try = 1729
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 111.94320000000002       try = 1730
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 112.05580000000002       try = 1731
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.87120000000002       try = 1732
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 112.61640000000003       try = 1733
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.85380000000002       try = 1734
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.54220000000002       try = 1735
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 105.6842                 try = 1736
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 111.60250000000002       try = 1737
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.68870000000003       try = 1738
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.9047                 try = 1739
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 106.89550000000001       try = 1740
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.65030000000003       try = 1741
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 106.06310000000002       try = 1742
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 105.85490000000003       try = 1743
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 101.1723                 try = 1744
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 128.08830000000003       try = 1745
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 117.72770000000001       try = 1746
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 118.27310000000001       try = 1747
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 106.81710000000001       try = 1748
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 119.03510000000003       try = 1749
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 107.00110000000002       try = 1750
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 107.12230000000001       try = 1751
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 93.99289999999999        try = 1752
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 117.58540000000002       try = 1753
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 106.40020000000001       try = 1754
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 107.04899999999999       try = 1755
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 94.7684                  try = 1756
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 106.99600000000001       try = 1757
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 94.13740000000003        try = 1758
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 94.36200000000001        try = 1759
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 80.40800000000002        try = 1760
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 139.297                  try = 1761
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 125.89520000000003       try = 1762
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 126.54920000000003       try = 1763
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 112.05200000000002       try = 1764
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 126.65320000000003       try = 1765
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 111.57800000000002       try = 1766
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 111.80780000000003       try = 1767
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 95.6372                  try = 1768
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 125.68670000000003       try = 1769
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 111.46030000000003       try = 1770
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 112.21770000000002       try = 1771
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 96.89590000000001        try = 1772
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 111.50670000000002       try = 1773
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 95.60690000000002        try = 1774
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 95.94010000000002        try = 1775
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 78.9449                  try = 1776
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 148.98270000000002       try = 1777
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 126.30950000000003       try = 1778
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 127.39630000000004       try = 1779
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 103.6277                 try = 1780
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 127.70170000000005       try = 1781
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 103.35510000000001       try = 1782
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 104.0177                 try = 1783
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 78.57570000000001        try = 1784
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 126.29940000000003       try = 1785
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 102.80160000000002       try = 1786
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 103.99180000000001       try = 1787
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 79.39860000000002        try = 1788
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 103.48220000000002       try = 1789
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 78.311                   try = 1790
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 79.07700000000001        try = 1791
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 52.810399999999994       try = 1792
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 78.12200000000001        try = 1793
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 92.4122                  try = 1794
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 92.0598                  try = 1795
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 105.2546                 try = 1796
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 93.097                   try = 1797
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 105.7138                 try = 1798
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 104.9372                 try = 1799
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 116.45859999999999       try = 1800
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 92.03070000000001        try = 1801
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 105.49630000000002       try = 1802
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 105.24730000000001       try = 1803
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 117.6175                 try = 1804
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 105.46950000000001       try = 1805
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 117.26170000000002       try = 1806
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 116.58850000000002       try = 1807
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 127.28529999999999       try = 1808
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 100.4971                 try = 1809
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 105.5159                 try = 1810
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 105.5963                 try = 1811
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.51970000000001       try = 1812
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 106.83490000000002       try = 1813
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 110.18030000000002       try = 1814
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.8365                 try = 1815
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 112.08650000000002       try = 1816
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 105.33280000000002       try = 1817
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.52700000000003       try = 1818
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.71080000000002       try = 1819
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 112.80960000000002       try = 1820
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 110.13440000000003       try = 1821
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 112.65520000000002       try = 1822
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 112.41480000000003       try = 1823
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 113.84020000000002       try = 1824
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 103.774                  try = 1825
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 105.7516                 try = 1826
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 105.9406                 try = 1827
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.8228                 try = 1828
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.5212                 try = 1829
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.82540000000002       try = 1830
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.59020000000001       try = 1831
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 105.799                  try = 1832
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 105.5023                 try = 1833
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.65530000000001       try = 1834
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.94770000000001       try = 1835
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 107.0053                 try = 1836
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.71330000000002       try = 1837
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.19290000000002       try = 1838
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 106.06110000000002       try = 1839
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 104.44530000000002       try = 1840
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 120.77890000000002       try = 1841
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 113.48510000000002       try = 1842
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 114.10690000000001       try = 1843
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 105.71770000000002       try = 1844
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 114.88890000000002       try = 1845
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 105.92170000000002       try = 1846
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 106.11930000000002       try = 1847
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 96.05669999999999        try = 1848
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 113.43420000000002       try = 1849
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 105.31580000000001       try = 1850
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 106.04100000000001       try = 1851
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 96.82719999999999        try = 1852
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 106.00800000000002       try = 1853
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 96.21620000000001        try = 1854
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 96.51720000000002        try = 1855
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 85.63                    try = 1856
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 105.6775                 try = 1857
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 106.9339                 try = 1858
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 106.9647                 try = 1859
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.1257                 try = 1860
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.9041                 try = 1861
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.4871                 try = 1862
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.0937                 try = 1863
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 105.5813                 try = 1864
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 106.61540000000002       try = 1865
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.04720000000002       try = 1866
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.18140000000001       try = 1867
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 106.51779999999998       try = 1868
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 107.30580000000002       try = 1869
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 106.06420000000001       try = 1870
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 105.77420000000001       try = 1871
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 103.43719999999999       try = 1872
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 122.799                  try = 1873
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 114.784                  try = 1874
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 115.2476                 try = 1875
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 106.13719999999999       try = 1876
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 116.3884                 try = 1877
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 106.7                    try = 1878
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 106.7394                 try = 1879
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 95.95559999999999        try = 1880
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 114.66390000000001       try = 1881
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 105.82430000000001       try = 1882
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 106.39130000000002       try = 1883
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 96.45629999999998        try = 1884
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 106.71710000000002       try = 1885
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 96.2041                  try = 1886
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 96.3469                  try = 1887
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 84.73849999999999        try = 1888
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 128.8881                 try = 1889
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 117.8319                 try = 1890
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 118.40410000000001       try = 1891
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 106.2525                 try = 1892
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 118.88690000000001       try = 1893
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 106.1573                 try = 1894
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 106.3053                 try = 1895
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 92.4803                  try = 1896
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 117.64560000000002       try = 1897
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 105.76480000000002       try = 1898
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 106.44040000000001       try = 1899
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 93.4642                  try = 1900
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 106.10820000000001       try = 1901
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 92.554                   try = 1902
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 92.8054                  try = 1903
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 78.1558                  try = 1904
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 140.63939999999997       try = 1905
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 120.31180000000002       try = 1906
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 121.31680000000001       try = 1907
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 99.8938                  try = 1908
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 122.00100000000002       try = 1909
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 100.0                    try = 1910
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 100.5808                 try = 1911
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 77.48440000000001        try = 1912
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 120.32390000000002       try = 1913
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 99.1717                  try = 1914
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 100.2801                 try = 1915
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 78.0325                  try = 1916
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 100.14930000000001       try = 1917
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 77.3237                  try = 1918
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 78.00789999999999        try = 1919
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 54.08689999999999        try = 1920
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 101.30350000000001       try = 1921
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 104.97290000000001       try = 1922
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 105.0629                 try = 1923
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 107.63690000000001       try = 1924
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 105.9055                 try = 1925
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 107.90150000000001       try = 1926
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 107.56730000000002       try = 1927
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 108.4679                 try = 1928
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 104.70320000000001       try = 1929
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 107.54800000000003       try = 1930
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 107.74140000000003       try = 1931
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 109.49080000000001       try = 1932
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 107.76900000000002       try = 1933
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 108.94040000000003       try = 1934
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 108.70960000000002       try = 1935
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 108.78560000000002       try = 1936
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 120.05100000000002       try = 1937
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 114.44900000000001       try = 1938
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 114.97180000000002       try = 1939
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.27440000000001       try = 1940
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 116.01580000000001       try = 1941
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.74040000000002       try = 1942
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.83900000000001       try = 1943
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 100.4682                 try = 1944
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 114.37770000000002       try = 1945
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 107.95110000000003       try = 1946
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.57730000000002       try = 1947
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 101.0553                 try = 1948
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.80630000000002       try = 1949
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 100.70630000000003       try = 1950
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 100.90830000000001       try = 1951
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 91.71290000000002        try = 1952
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 124.71050000000002       try = 1953
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 116.06730000000002       try = 1954
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 116.69870000000002       try = 1955
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 106.96010000000001       try = 1956
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 117.08470000000001       try = 1957
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 106.76810000000002       try = 1958
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 106.97530000000002       try = 1959
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 95.5633                  try = 1960
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 115.92980000000003       try = 1961
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 106.46200000000003       try = 1962
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 107.19680000000002       try = 1963
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 96.6336                  try = 1964
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 106.76780000000002       try = 1965
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 95.62660000000001        try = 1966
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 95.93720000000002        try = 1967
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 83.70060000000001        try = 1968
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 138.0878                 try = 1969
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 120.17320000000002       try = 1970
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 121.23740000000002       try = 1971
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 102.22740000000002       try = 1972
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 121.82480000000002       try = 1973
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 102.23680000000002       try = 1974
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 102.87680000000002       try = 1975
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 82.1934                  try = 1976
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 120.23410000000003       try = 1977
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 101.49490000000002       try = 1978
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 102.66250000000002       try = 1979
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 82.8279                  try = 1980
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 102.43490000000003       try = 1981
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 82.0223                  try = 1982
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 82.76570000000001        try = 1983
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 61.257699999999986       try = 1984
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 126.27440000000001       try = 1985
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 116.91000000000003       try = 1986
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 117.38320000000002       try = 1987
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 106.92340000000002       try = 1988
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 118.12800000000003       try = 1989
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 107.09020000000001       try = 1990
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 107.13920000000002       try = 1991
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 95.00600000000001        try = 1992
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 116.70330000000004       try = 1993
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 106.51430000000002       try = 1994
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 107.09090000000002       try = 1995
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 95.80650000000001        try = 1996
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 107.02070000000003       try = 1997
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 95.15830000000003        try = 1998
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 95.31070000000003        try = 1999
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 82.3529                  try = 2000
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 139.7683                 try = 2001
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 121.13250000000002       try = 2002
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 122.03850000000003       try = 2003
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 102.30730000000001       try = 2004
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 122.98470000000003       try = 2005
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 102.6755                 try = 2006
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 103.1573                 try = 2007
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 81.75269999999999        try = 2008
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 121.12420000000003       try = 2009
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 101.66380000000002       try = 2010
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 102.67320000000002       try = 2011
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 82.1174                  try = 2012
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 102.80440000000002       try = 2013
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 81.67060000000001        try = 2014
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 82.2558                  try = 2015
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 60.0266                  try = 2016
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 147.24                   try = 2017
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 125.56300000000002       try = 2018
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 126.5776                 try = 2019
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.8052                 try = 2020
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 126.86580000000002       try = 2021
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.51540000000001       try = 2022
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 104.10580000000002       try = 2023
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 79.66                    try = 2024
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 125.48850000000003       try = 2025
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 102.98690000000002       try = 2026
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 104.10490000000001       try = 2027
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 80.5079                  try = 2028
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.57810000000002       try = 2029
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 79.40310000000001        try = 2030
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 80.0969                  try = 2031
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 54.8265                  try = 2032
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 155.36370000000002       try = 2033
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 124.4153                 try = 2034
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 125.8627                 try = 2035
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 93.8189                  try = 2036
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 126.35230000000003       try = 2037
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 93.7305                  try = 2038
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 94.75370000000001        try = 2039
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 61.036500000000004       try = 2040
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 124.53920000000002       try = 2041
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 92.76620000000001        try = 2042
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 94.31700000000002        try = 2043
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 61.4486                  try = 2044
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 93.9916                  try = 2045
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 60.5452                  try = 2046
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 61.671800000000005       try = 2047
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 27.13                    try = 2048
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 27.13                    try = 2049
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 61.67179999999998        try = 2050
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 60.545199999999994       try = 2051
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 93.9916                  try = 2052
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 61.448599999999985       try = 2053
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 94.31700000000001        try = 2054
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 92.7662                  try = 2055
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 124.53920000000001       try = 2056
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 61.03649999999999        try = 2057
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 94.7537                  try = 2058
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 93.73049999999999        try = 2059
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 126.35230000000001       try = 2060
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 93.8189                  try = 2061
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 125.86270000000002       try = 2062
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 124.41530000000002       try = 2063
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 155.3637                 try = 2064
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 54.82649999999999        try = 2065
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 80.0969                  try = 2066
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 79.40310000000002        try = 2067
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.5781                 try = 2068
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 80.5079                  try = 2069
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 104.10490000000003       try = 2070
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 102.98690000000002       try = 2071
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 125.48850000000002       try = 2072
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 79.66                    try = 2073
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 104.10580000000003       try = 2074
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.51540000000001       try = 2075
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 126.86580000000001       try = 2076
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.80520000000001       try = 2077
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 126.57760000000003       try = 2078
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 125.56300000000002       try = 2079
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 147.23999999999995       try = 2080
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 60.02659999999999        try = 2081
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 82.25580000000001        try = 2082
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 81.67060000000001        try = 2083
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 102.80439999999999       try = 2084
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 82.11740000000002        try = 2085
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 102.6732                 try = 2086
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 101.6638                 try = 2087
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 121.12419999999999       try = 2088
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 81.7527                  try = 2089
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 103.15729999999999       try = 2090
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 102.67549999999999       try = 2091
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 122.98469999999998       try = 2092
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 102.3073                 try = 2093
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 122.03849999999998       try = 2094
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 121.1325                 try = 2095
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 139.7683                 try = 2096
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 82.35290000000002        try = 2097
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 95.31070000000001        try = 2098
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 95.15830000000001        try = 2099
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 107.0207                 try = 2100
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 95.8065                  try = 2101
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 107.0909                 try = 2102
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 106.5143                 try = 2103
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 116.70330000000001       try = 2104
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 95.006                   try = 2105
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 107.1392                 try = 2106
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 107.0902                 try = 2107
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 118.12799999999999       try = 2108
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 106.9234                 try = 2109
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 117.38319999999999       try = 2110
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 116.91                   try = 2111
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 126.27439999999999       try = 2112
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 61.25769999999998        try = 2113
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 82.7657                  try = 2114
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 82.0223                  try = 2115
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 102.43489999999998       try = 2116
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 82.8279                  try = 2117
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 102.6625                 try = 2118
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 101.4949                 try = 2119
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 120.23409999999998       try = 2120
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 82.1934                  try = 2121
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 102.8768                 try = 2122
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 102.2368                 try = 2123
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 121.82479999999997       try = 2124
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 102.2274                 try = 2125
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 121.2374                 try = 2126
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 120.1732                 try = 2127
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 138.08780000000002       try = 2128
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 83.7006                  try = 2129
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 95.93720000000002        try = 2130
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 95.62660000000001        try = 2131
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 106.76780000000002       try = 2132
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 96.63360000000002        try = 2133
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 107.19680000000001       try = 2134
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 106.46200000000002       try = 2135
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 115.92980000000001       try = 2136
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 95.5633                  try = 2137
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 106.97530000000002       try = 2138
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 106.76810000000002       try = 2139
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 117.08470000000001       try = 2140
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 106.9601                 try = 2141
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 116.6987                 try = 2142
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 116.0673                 try = 2143
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 124.71049999999998       try = 2144
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 91.7129                  try = 2145
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 100.90830000000001       try = 2146
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 100.7063                 try = 2147
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.80630000000001       try = 2148
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 101.05530000000002       try = 2149
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.57730000000001       try = 2150
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 107.95110000000001       try = 2151
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 114.37770000000002       try = 2152
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 100.46820000000001       try = 2153
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.83900000000001       try = 2154
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.7404                 try = 2155
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 116.0158                 try = 2156
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.27440000000001       try = 2157
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 114.9718                 try = 2158
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 114.44900000000001       try = 2159
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 120.05100000000003       try = 2160
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 108.78560000000002       try = 2161
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 108.70960000000002       try = 2162
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 108.94040000000003       try = 2163
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 107.76900000000002       try = 2164
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 109.49080000000002       try = 2165
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 107.7414                 try = 2166
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 107.54800000000002       try = 2167
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 104.70320000000001       try = 2168
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 108.46790000000001       try = 2169
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 107.5673                 try = 2170
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 107.9015                 try = 2171
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 105.90550000000002       try = 2172
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 107.6369                 try = 2173
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 105.0629                 try = 2174
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 104.97290000000001       try = 2175
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 101.30350000000001       try = 2176
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 54.08689999999999        try = 2177
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 78.0079                  try = 2178
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 77.32370000000002        try = 2179
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 100.14929999999998       try = 2180
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 78.03250000000001        try = 2181
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 100.2801                 try = 2182
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 99.1717                  try = 2183
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 120.32390000000001       try = 2184
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 77.48440000000001        try = 2185
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 100.5808                 try = 2186
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 100.0                    try = 2187
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 122.00099999999999       try = 2188
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 99.89380000000001        try = 2189
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 121.31680000000001       try = 2190
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 120.31179999999999       try = 2191
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 140.6394                 try = 2192
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 78.15580000000001        try = 2193
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 92.80540000000002        try = 2194
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 92.554                   try = 2195
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 106.10820000000002       try = 2196
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 93.4642                  try = 2197
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 106.44040000000003       try = 2198
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 105.76480000000001       try = 2199
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 117.64560000000002       try = 2200
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 92.4803                  try = 2201
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 106.30530000000002       try = 2202
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 106.1573                 try = 2203
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 118.8869                 try = 2204
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 106.25250000000001       try = 2205
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 118.40410000000001       try = 2206
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 117.83190000000002       try = 2207
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 128.8881                 try = 2208
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 84.7385                  try = 2209
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 96.34689999999999        try = 2210
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 96.20409999999998        try = 2211
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 106.71709999999997       try = 2212
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 96.4563                  try = 2213
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 106.39129999999999       try = 2214
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 105.8243                 try = 2215
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 114.6639                 try = 2216
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 95.9556                  try = 2217
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 106.73939999999999       try = 2218
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 106.69999999999997       try = 2219
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 116.38839999999996       try = 2220
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 106.13719999999999       try = 2221
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 115.24759999999998       try = 2222
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 114.78399999999999       try = 2223
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 122.79899999999999       try = 2224
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 103.4372                 try = 2225
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 105.77420000000001       try = 2226
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 106.06420000000001       try = 2227
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.3058                 try = 2228
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 106.51780000000001       try = 2229
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.1814                 try = 2230
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.04719999999999       try = 2231
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 106.6154                 try = 2232
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 105.5813                 try = 2233
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.09369999999998       try = 2234
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.48709999999998       try = 2235
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.90409999999999       try = 2236
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 107.1257                 try = 2237
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 106.9647                 try = 2238
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 106.9339                 try = 2239
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 105.6775                 try = 2240
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 85.63000000000001        try = 2241
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 96.5172                  try = 2242
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 96.2162                  try = 2243
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 106.00800000000001       try = 2244
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 96.82719999999999        try = 2245
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 106.04100000000003       try = 2246
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 105.31580000000001       try = 2247
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 113.4342                 try = 2248
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 96.05669999999999        try = 2249
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 106.1193                 try = 2250
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 105.92169999999999       try = 2251
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 114.88889999999999       try = 2252
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 105.71770000000002       try = 2253
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 114.10690000000001       try = 2254
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 113.48510000000002       try = 2255
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 120.77890000000001       try = 2256
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 104.4453                 try = 2257
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.06110000000002       try = 2258
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.19290000000001       try = 2259
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.71329999999999       try = 2260
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 107.0053                 try = 2261
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.94770000000001       try = 2262
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.65530000000001       try = 2263
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 105.5023                 try = 2264
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 105.799                  try = 2265
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.59020000000001       try = 2266
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.82539999999999       try = 2267
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.52120000000001       try = 2268
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 106.82280000000002       try = 2269
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 105.94060000000002       try = 2270
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 105.75160000000001       try = 2271
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 103.77400000000002       try = 2272
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 113.84020000000001       try = 2273
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 112.4148                 try = 2274
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 112.65520000000001       try = 2275
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 110.13440000000001       try = 2276
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 112.80960000000002       try = 2277
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.71080000000002       try = 2278
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.52700000000002       try = 2279
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 105.3328                 try = 2280
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 112.0865                 try = 2281
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.83650000000002       try = 2282
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 110.18029999999999       try = 2283
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 106.83489999999999       try = 2284
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.5197                 try = 2285
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 105.5963                 try = 2286
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 105.5159                 try = 2287
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 100.4971                 try = 2288
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 127.28530000000002       try = 2289
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 116.58850000000001       try = 2290
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 117.2617                 try = 2291
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 105.46950000000001       try = 2292
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 117.61750000000002       try = 2293
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 105.24730000000002       try = 2294
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 105.4963                 try = 2295
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 92.03070000000002        try = 2296
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 116.45860000000002       try = 2297
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 104.9372                 try = 2298
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 105.71379999999999       try = 2299
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 93.097                   try = 2300
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 105.25460000000001       try = 2301
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 92.05980000000001        try = 2302
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 92.41220000000001        try = 2303
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 78.12199999999999        try = 2304
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 52.81039999999999        try = 2305
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 79.077                   try = 2306
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 78.311                   try = 2307
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 103.48220000000002       try = 2308
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 79.3986                  try = 2309
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 103.99180000000003       try = 2310
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 102.80160000000004       try = 2311
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 126.29940000000003       try = 2312
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 78.5757                  try = 2313
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 104.01770000000003       try = 2314
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 103.35510000000002       try = 2315
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 127.70170000000002       try = 2316
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 103.62770000000003       try = 2317
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 127.39630000000004       try = 2318
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 126.30950000000003       try = 2319
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 148.9827                 try = 2320
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 78.94490000000002        try = 2321
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 95.94010000000004        try = 2322
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 95.60690000000004        try = 2323
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 111.50670000000004       try = 2324
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 96.89590000000003        try = 2325
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 112.21770000000004       try = 2326
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 111.46030000000003       try = 2327
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 125.68670000000002       try = 2328
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 95.63720000000002        try = 2329
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 111.80780000000004       try = 2330
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 111.57800000000003       try = 2331
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 126.65320000000003       try = 2332
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 112.05200000000004       try = 2333
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 126.54920000000003       try = 2334
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 125.89520000000005       try = 2335
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 139.29699999999997       try = 2336
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 80.40799999999999        try = 2337
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 94.36200000000002        try = 2338
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 94.13740000000003        try = 2339
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 106.99600000000002       try = 2340
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 94.76840000000003        try = 2341
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 107.04900000000002       try = 2342
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 106.40020000000003       try = 2343
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 117.5854                 try = 2344
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 93.99290000000002        try = 2345
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 107.12230000000002       try = 2346
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 107.00110000000002       try = 2347
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 119.0351                 try = 2348
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 106.81710000000004       try = 2349
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 118.2731                 try = 2350
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 117.72770000000003       try = 2351
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 128.0883                 try = 2352
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 101.17230000000002       try = 2353
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 105.85490000000004       try = 2354
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 106.06310000000003       try = 2355
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.65030000000002       try = 2356
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 106.89550000000006       try = 2357
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.90470000000002       try = 2358
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.68870000000001       try = 2359
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 111.60250000000002       try = 2360
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 105.68420000000003       try = 2361
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.54220000000002       try = 2362
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.8538                 try = 2363
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 112.6164                 try = 2364
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.87120000000003       try = 2365
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 112.0558                 try = 2366
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 111.94320000000002       try = 2367
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 113.03240000000001       try = 2368
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 81.66550000000001        try = 2369
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 94.89830000000002        try = 2370
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 94.51550000000002        try = 2371
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 106.65290000000002       try = 2372
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 95.50530000000002        try = 2373
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 107.06470000000002       try = 2374
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 106.25770000000003       try = 2375
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 116.7217                 try = 2376
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 94.46000000000002        try = 2377
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 106.86820000000003       try = 2378
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 106.58880000000002       try = 2379
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 117.90160000000002       try = 2380
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 106.76360000000004       try = 2381
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 117.4984                 try = 2382
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 116.79480000000001       try = 2383
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 126.4342                 try = 2384
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 102.5464                 try = 2385
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 106.50780000000002       try = 2386
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 106.55780000000003       try = 2387
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.42380000000003       try = 2388
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 107.74900000000004       try = 2389
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 110.03700000000002       try = 2390
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.6628                 try = 2391
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 110.85540000000002       try = 2392
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 106.26790000000003       try = 2393
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.40470000000002       try = 2394
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.55810000000001       try = 2395
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 111.59950000000002       try = 2396
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.93430000000002       try = 2397
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 111.39770000000001       try = 2398
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 111.1269                 try = 2399
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 111.4949                 try = 2400
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 106.8217                 try = 2401
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.74190000000003       try = 2402
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.90050000000002       try = 2403
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.72530000000002       try = 2404
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 108.43370000000003       try = 2405
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.68050000000002       try = 2406
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.41490000000002       try = 2407
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 105.56630000000001       try = 2408
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.43580000000003       try = 2409
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.53140000000002       try = 2410
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.79340000000002       try = 2411
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 106.7936                 try = 2412
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.51160000000002       try = 2413
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 105.93380000000002       try = 2414
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 105.7716                 try = 2415
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 103.09840000000003       try = 2416
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 122.33240000000002       try = 2417
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 113.98120000000003       try = 2418
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 114.57260000000002       try = 2419
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 105.12600000000003       try = 2420
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 115.30720000000002       try = 2421
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 105.28260000000003       try = 2422
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 105.44980000000001       try = 2423
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 94.3298                  try = 2424
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 113.87350000000002       try = 2425
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 104.69770000000003       try = 2426
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 105.39250000000001       try = 2427
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 95.1213                  try = 2428
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 105.31210000000002       try = 2429
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 94.4629                  try = 2430
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 94.73350000000002        try = 2431
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 82.78889999999998        try = 2432
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 76.54230000000001        try = 2433
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 92.18810000000003        try = 2434
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 91.86450000000002        try = 2435
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 106.41490000000003       try = 2436
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 92.75750000000002        try = 2437
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 106.72990000000003       try = 2438
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 105.98210000000003       try = 2439
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 118.85910000000003       try = 2440
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 91.79860000000002        try = 2441
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 106.61980000000003       try = 2442
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 106.39960000000004       try = 2443
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 120.1254                 try = 2444
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 106.47760000000004       try = 2445
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 119.62540000000003       try = 2446
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 118.98100000000002       try = 2447
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 131.03340000000003       try = 2448
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 99.04920000000004        try = 2449
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 105.42360000000005       try = 2450
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 105.53280000000004       try = 2451
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 110.81180000000005       try = 2452
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 106.62720000000004       try = 2453
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 111.32820000000004       try = 2454
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 111.01320000000004       try = 2455
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 114.61880000000005       try = 2456
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 105.23250000000004       try = 2457
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 110.78230000000003       try = 2458
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 110.99490000000003       try = 2459
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 115.44930000000002       try = 2460
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 111.27430000000004       try = 2461
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 115.15070000000004       try = 2462
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 114.93910000000004       try = 2463
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 117.72010000000003       try = 2464
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 101.89490000000004       try = 2465
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 105.22810000000003       try = 2466
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 105.44590000000002       try = 2467
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.68370000000002       try = 2468
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 105.88230000000003       try = 2469
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.54210000000005       try = 2470
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.33570000000002       try = 2471
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.90010000000002       try = 2472
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 104.97080000000003       try = 2473
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.47940000000003       try = 2474
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.80060000000002       try = 2475
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 109.21379999999999       try = 2476
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.42200000000004       try = 2477
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 108.25720000000001       try = 2478
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 108.15420000000002       try = 2479
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.894                  try = 2480
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 119.03160000000004       try = 2481
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 113.09340000000005       try = 2482
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 113.74400000000001       try = 2483
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 106.71040000000004       try = 2484
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 114.38180000000006       try = 2485
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 106.77020000000005       try = 2486
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 106.99660000000003       try = 2487
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 98.28960000000001        try = 2488
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 113.03450000000002       try = 2489
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 106.27170000000002       try = 2490
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 107.02570000000001       try = 2491
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 99.16749999999999        try = 2492
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 106.84850000000003       try = 2493
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 98.41230000000002        try = 2494
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 98.74210000000002        try = 2495
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 89.21050000000001        try = 2496
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 102.81280000000004       try = 2497
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 105.42480000000003       try = 2498
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 105.48440000000002       try = 2499
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 107.00100000000003       try = 2500
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 106.27960000000003       try = 2501
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 107.21820000000004       try = 2502
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 106.85360000000001       try = 2503
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 106.69680000000001       try = 2504
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 105.09830000000004       try = 2505
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 106.88570000000003       try = 2506
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 107.04870000000001       try = 2507
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 107.74070000000002       try = 2508
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 107.02890000000004       try = 2509
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 107.14290000000003       try = 2510
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 106.88170000000004       try = 2511
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 105.90030000000002       try = 2512
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 120.06610000000002       try = 2513
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 113.40670000000001       try = 2514
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 113.89910000000002       try = 2515
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 106.14430000000003       try = 2516
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 114.89570000000003       try = 2517
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 106.56290000000004       try = 2518
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 106.63110000000003       try = 2519
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 97.20290000000003        try = 2520
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 113.27860000000003       try = 2521
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 105.79460000000003       try = 2522
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 106.39040000000003       try = 2523
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 97.811                   try = 2524
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 106.57200000000003       try = 2525
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 97.41460000000004        try = 2526
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 97.58620000000002        try = 2527
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 87.33340000000001        try = 2528
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 125.72400000000002       try = 2529
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 116.02340000000001       try = 2530
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 116.62440000000001       try = 2531
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 105.82840000000002       try = 2532
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 116.96300000000004       try = 2533
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 105.58900000000004       try = 2534
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 105.76580000000003       try = 2535
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 93.29640000000002        try = 2536
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 115.82910000000003       try = 2537
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 105.30390000000001       try = 2538
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 106.00830000000002       try = 2539
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 94.3877                  try = 2540
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 105.53190000000004       try = 2541
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 93.33330000000004        try = 2542
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 93.61350000000002        try = 2543
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 80.3195                  try = 2544
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 137.6071                 try = 2545
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 118.63510000000004       try = 2546
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 119.66890000000002       try = 2547
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 99.60150000000003        try = 2548
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 120.20890000000003       try = 2549
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 99.56350000000003        try = 2550
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 100.17310000000003       try = 2551
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 78.43230000000001        try = 2552
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 118.63920000000002       try = 2553
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 98.84260000000002        try = 2554
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 99.97980000000001        try = 2555
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 79.0878                  try = 2556
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 99.70480000000003        try = 2557
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 78.2348                  try = 2558
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 78.9478                  try = 2559
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 56.3824                  try = 2560
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 55.22129999999999        try = 2561
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 78.6455                  try = 2562
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 77.8921                  try = 2563
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 100.22089999999997       try = 2564
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 78.69930000000001        try = 2565
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 100.45009999999999       try = 2566
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 99.2725                  try = 2567
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 119.92789999999998       try = 2568
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 78.07339999999999        try = 2569
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 100.673                  try = 2570
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 100.023                  try = 2571
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 121.5272                 try = 2572
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 100.01520000000001       try = 2573
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 120.9414                 try = 2574
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 119.8672                 try = 2575
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 139.69799999999998       try = 2576
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 79.014                   try = 2577
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 93.16680000000001        try = 2578
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 92.8462                  try = 2579
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 105.90360000000001       try = 2580
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 93.8548                  try = 2581
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 106.33420000000002       try = 2582
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 105.58940000000001       try = 2583
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 116.97340000000001       try = 2584
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 92.7931                  try = 2585
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 106.12130000000002       try = 2586
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 105.90410000000001       try = 2587
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 118.13690000000003       try = 2588
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 106.09770000000003       try = 2589
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 117.75250000000005       try = 2590
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 117.11110000000004       try = 2591
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 127.6705                 try = 2592
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 85.6359                  try = 2593
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 96.74749999999999        try = 2594
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 96.53549999999998        try = 2595
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 106.55169999999998       try = 2596
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 96.8861                  try = 2597
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 106.3243                 try = 2598
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 105.68809999999999       try = 2599
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 114.03089999999997       try = 2600
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 96.30759999999998        try = 2601
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 106.59459999999999       try = 2602
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 106.48599999999999       try = 2603
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 115.67759999999998       try = 2604
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 106.0216                 try = 2605
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 114.6352                 try = 2606
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 114.1024                 try = 2607
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 121.6206                 try = 2608
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 104.05839999999999       try = 2609
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 105.89860000000002       try = 2610
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.1194                 try = 2611
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.86419999999998       try = 2612
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.67140000000002       try = 2613
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.8382                 try = 2614
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.63479999999998       try = 2615
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 105.7062                 try = 2616
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 105.65710000000001       try = 2617
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.6727                 try = 2618
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.99689999999998       try = 2619
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.9171                 try = 2620
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.7339                 try = 2621
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 106.07610000000001       try = 2622
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 105.9761                 try = 2623
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 104.22290000000001       try = 2624
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 87.42020000000001        try = 2625
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 97.81059999999998        try = 2626
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 97.44039999999998        try = 2627
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 106.73539999999998       try = 2628
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 98.14979999999998        try = 2629
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 106.8668                 try = 2630
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 106.0724                 try = 2631
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 113.69399999999999       try = 2632
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 97.30149999999999        try = 2633
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 106.8673                 try = 2634
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 106.60049999999998       try = 2635
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 115.0709                 try = 2636
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 106.49490000000002       try = 2637
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 114.38730000000001       try = 2638
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 113.69630000000001       try = 2639
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 120.49329999999999       try = 2640
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 105.95929999999998       try = 2641
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.0783                 try = 2642
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.1409                 try = 2643
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.1645                 try = 2644
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 108.05170000000003       try = 2645
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.49730000000001       try = 2646
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.1357                 try = 2647
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 105.48590000000002       try = 2648
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 106.76760000000002       try = 2649
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.062                  try = 2650
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.22799999999998       try = 2651
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 106.427                  try = 2652
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.32380000000002       try = 2653
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 105.94480000000001       try = 2654
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 105.68660000000003       try = 2655
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 103.21220000000001       try = 2656
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 115.3934                 try = 2657
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 113.47120000000001       try = 2658
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 113.6424                 try = 2659
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 110.6248                 try = 2660
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 113.89520000000002       try = 2661
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 110.2996                 try = 2662
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 110.0466                 try = 2663
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 105.3556                 try = 2664
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 113.0943                 try = 2665
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 110.34750000000001       try = 2666
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 110.62209999999999       try = 2667
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 106.7799                 try = 2668
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 110.05990000000001       try = 2669
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 105.6397                 try = 2670
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 105.49010000000001       try = 2671
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 99.97450000000002        try = 2672
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 128.56230000000002       try = 2673
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 117.3687                 try = 2674
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 117.9727                 try = 2675
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 105.6837                 try = 2676
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 118.42690000000002       try = 2677
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 105.55990000000003       try = 2678
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 105.73970000000001       try = 2679
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 91.7773                  try = 2680
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 117.19020000000002       try = 2681
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 105.17200000000001       try = 2682
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 105.8794                 try = 2683
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 92.7658                  try = 2684
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 105.5186                 try = 2685
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 91.82700000000001        try = 2686
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 92.1102                  try = 2687
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 77.3232                  try = 2688
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 81.2402                  try = 2689
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 94.0436                  try = 2690
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 93.73259999999999        try = 2691
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 105.4406                 try = 2692
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 94.3452                  try = 2693
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 105.47520000000002       try = 2694
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 104.74000000000001       try = 2695
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 114.77459999999999       try = 2696
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 93.5833                  try = 2697
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 105.5621                 try = 2698
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 105.35449999999999       try = 2699
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 116.23789999999998       try = 2700
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 105.15210000000002       try = 2701
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 115.45750000000001       try = 2702
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 114.82570000000001       try = 2703
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 124.03570000000002       try = 2704
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 101.4053                 try = 2705
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 104.93730000000001       try = 2706
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 105.0591                 try = 2707
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 107.49570000000001       try = 2708
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 105.87310000000002       try = 2709
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 107.73170000000002       try = 2710
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 107.4293                 try = 2711
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.19250000000004       try = 2712
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 104.67540000000002       try = 2713
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 107.38280000000002       try = 2714
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 107.608                  try = 2715
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 109.22000000000003       try = 2716
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 107.60700000000003       try = 2717
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.64100000000005       try = 2718
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.44200000000004       try = 2719
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.38060000000003       try = 2720
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.40979999999999       try = 2721
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.9006                 try = 2722
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.13099999999999       try = 2723
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.5264                 try = 2724
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.28700000000002       try = 2725
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.10440000000001       try = 2726
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 108.91059999999999       try = 2727
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 106.6326                 try = 2728
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.5725                 try = 2729
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.2387                 try = 2730
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.57249999999998       try = 2731
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 108.14329999999997       try = 2732
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 108.91350000000001       try = 2733
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 106.9063                 try = 2734
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 106.81589999999998       try = 2735
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 103.71329999999999       try = 2736
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 124.2047                 try = 2737
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 115.42410000000001       try = 2738
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 116.08730000000001       try = 2739
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 106.21130000000001       try = 2740
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 116.44470000000001       try = 2741
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 105.99070000000003       try = 2742
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 106.22970000000002       try = 2743
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 94.6803                  try = 2744
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 115.29440000000001       try = 2745
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 105.68920000000001       try = 2746
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 106.4558                 try = 2747
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 95.75519999999997        try = 2748
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 105.99820000000003       try = 2749
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 94.7196                  try = 2750
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 95.062                   try = 2751
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 82.68799999999999        try = 2752
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 110.8545                 try = 2753
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 110.6241                 try = 2754
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 110.6963                 try = 2755
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 109.3705                 try = 2756
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 111.21110000000002       try = 2757
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 109.3073                 try = 2758
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 108.95530000000001       try = 2759
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 105.9561                 try = 2760
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 110.22680000000001       try = 2761
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 109.1718                 try = 2762
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 109.3474                 try = 2763
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 107.197                  try = 2764
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 109.04720000000002       try = 2765
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 106.31880000000001       try = 2766
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 106.07020000000001       try = 2767
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 102.24640000000001       try = 2768
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 125.766                  try = 2769
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 116.2642                 try = 2770
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 116.76919999999998       try = 2771
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 106.172                  try = 2772
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 117.48540000000001       try = 2773
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 106.31020000000002       try = 2774
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 106.39100000000002       try = 2775
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 94.12040000000002        try = 2776
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 116.06530000000001       try = 2777
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 105.73890000000002       try = 2778
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 106.34729999999999       try = 2779
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 94.9255                  try = 2780
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 106.24850000000002       try = 2781
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 94.24870000000003        try = 2782
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 94.43290000000002        try = 2783
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 81.3377                  try = 2784
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 136.5827                 try = 2785
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 124.03970000000001       try = 2786
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 124.65329999999999       try = 2787
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 111.0149                 try = 2788
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 124.71150000000003       try = 2789
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 110.49510000000001       try = 2790
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 110.6845                 try = 2791
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 95.3727                  try = 2792
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 123.7746                 try = 2793
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 110.407                  try = 2794
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 111.124                  try = 2795
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 96.66099999999999        try = 2796
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 110.36720000000003       try = 2797
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 95.32620000000001        try = 2798
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 95.619                   try = 2799
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 79.48259999999999        try = 2800
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 146.124                  try = 2801
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 124.30960000000003       try = 2802
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 125.35600000000002       try = 2803
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 102.4462                 try = 2804
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 125.61560000000004       try = 2805
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 102.12780000000002       try = 2806
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 102.75                   try = 2807
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 78.16680000000001        try = 2808
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 124.24290000000002       try = 2809
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 101.60390000000001       try = 2810
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 102.7537                 try = 2811
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 79.0193                  try = 2812
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 102.19830000000002       try = 2813
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 77.88589999999999        try = 2814
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 78.61149999999999        try = 2815
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 53.2037                  try = 2816
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 77.35770000000001        try = 2817
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 92.5067                  try = 2818
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 92.11389999999999        try = 2819
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 106.16749999999999       try = 2820
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 93.10529999999999        try = 2821
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 106.58090000000001       try = 2822
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 105.7639                 try = 2823
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 118.14409999999998       try = 2824
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 92.06859999999999        try = 2825
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 106.39300000000001       try = 2826
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 106.1036                 try = 2827
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 119.33259999999999       try = 2828
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 106.28000000000002       try = 2829
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 118.93100000000001       try = 2830
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 118.21740000000003       try = 2831
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 129.773                  try = 2832
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 99.5884                  try = 2833
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 105.46600000000001       try = 2834
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 105.506                  try = 2835
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.2882                 try = 2836
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 106.69880000000002       try = 2837
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.903                  try = 2838
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.51880000000001       try = 2839
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 113.62760000000002       try = 2840
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 105.22630000000002       try = 2841
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.2793                 try = 2842
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.4227                 try = 2843
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 114.3803                 try = 2844
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.80050000000003       try = 2845
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 114.18010000000004       try = 2846
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 113.89930000000003       try = 2847
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 116.18350000000002       try = 2848
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 102.47329999999998       try = 2849
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 105.30969999999999       try = 2850
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 105.45829999999998       try = 2851
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.19929999999998       try = 2852
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 105.9931                 try = 2853
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.15610000000001       try = 2854
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 106.8805                 try = 2855
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 106.94809999999998       try = 2856
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 105.00379999999998       try = 2857
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.0156                 try = 2858
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.2676                 try = 2859
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 108.18399999999998       try = 2860
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 106.98740000000002       try = 2861
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.3258                 try = 2862
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.15360000000001       try = 2863
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 106.39659999999999       try = 2864
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 119.33380000000001       try = 2865
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 112.89880000000001       try = 2866
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 113.4802                 try = 2867
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 105.94980000000001       try = 2868
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 114.21640000000002       try = 2869
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 106.10800000000002       try = 2870
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 106.26520000000002       try = 2871
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 97.06139999999998        try = 2872
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 112.79130000000002       try = 2873
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 105.5317                 try = 2874
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 106.2165                 try = 2875
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 97.86149999999998        try = 2876
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 106.13770000000002       try = 2877
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 97.2047                  try = 2878
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 97.4653                  try = 2879
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 87.4369                  try = 2880
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 104.28399999999999       try = 2881
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 106.39919999999998       try = 2882
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 106.38959999999999       try = 2883
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.40939999999999       try = 2884
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.2832                 try = 2885
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.72500000000001       try = 2886
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.29119999999999       try = 2887
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 106.63759999999998       try = 2888
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 106.0241                 try = 2889
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.31470000000002       try = 2890
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.4085                 try = 2891
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.60369999999999       try = 2892
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.48710000000001       try = 2893
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 107.10430000000001       try = 2894
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 106.7739                 try = 2895
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 105.29570000000001       try = 2896
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 121.2611                 try = 2897
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 114.1049                 try = 2898
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 114.5281                 try = 2899
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 106.27650000000001       try = 2900
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 115.62310000000001       try = 2901
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 106.79350000000001       try = 2902
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 106.79250000000002       try = 2903
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 96.86749999999999        try = 2904
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 113.92820000000002       try = 2905
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 105.94740000000002       try = 2906
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 106.47400000000002       try = 2907
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 97.39779999999999        try = 2908
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 106.75400000000003       try = 2909
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 97.0998                  try = 2910
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 97.2022                  try = 2911
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 86.4526                  try = 2912
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 126.95819999999999       try = 2913
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 116.7608                 try = 2914
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 117.2926                 try = 2915
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 105.9998                 try = 2916
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 117.7296                 try = 2917
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 105.8588                 try = 2918
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 105.9664                 try = 2919
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 93.00019999999999        try = 2920
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 116.51790000000001       try = 2921
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 105.4959                 try = 2922
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 106.1311                 try = 2923
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 94.01369999999999        try = 2924
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 105.75310000000002       try = 2925
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 93.0577                  try = 2926
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 93.2687                  try = 2927
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 79.47789999999999        try = 2928
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 138.5651                 try = 2929
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 119.09630000000001       try = 2930
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 120.0609                 try = 2931
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 99.49669999999999        try = 2932
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 120.69930000000002       try = 2933
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 99.5571                  try = 2934
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 100.0975                 try = 2935
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 77.85989999999998        try = 2936
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 119.05180000000001       try = 2937
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 98.75840000000001        try = 2938
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 99.8264                  try = 2939
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 78.43759999999999        try = 2940
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 99.64980000000001        try = 2941
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 77.68299999999999        try = 2942
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 78.32679999999999        try = 2943
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 55.264599999999994       try = 2944
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 100.15159999999999       try = 2945
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 104.67980000000001       try = 2946
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 104.7294                 try = 2947
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.16220000000001       try = 2948
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 105.52620000000002       try = 2949
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.38100000000001       try = 2950
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.00640000000001       try = 2951
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 109.76580000000003       try = 2952
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 104.35350000000001       try = 2953
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.05710000000002       try = 2954
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.21010000000003       try = 2955
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 110.81830000000001       try = 2956
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.19190000000003       try = 2957
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 110.22210000000003       try = 2958
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 109.95090000000003       try = 2959
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 110.88570000000003       try = 2960
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 118.75470000000003       try = 2961
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 114.01150000000003       try = 2962
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 114.49390000000002       try = 2963
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 108.65530000000003       try = 2964
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 115.49210000000004       try = 2965
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 109.07550000000002       try = 2966
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 109.13370000000003       try = 2967
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 101.6217                 try = 2968
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 113.88360000000003       try = 2969
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 108.31580000000002       try = 2970
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 108.90160000000003       try = 2971
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 102.2384                 try = 2972
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 109.08480000000004       try = 2973
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 101.84360000000004       try = 2974
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 102.00520000000003       try = 2975
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 93.66860000000004        try = 2976
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 123.02220000000001       try = 2977
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 115.23780000000001       try = 2978
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 115.82880000000002       try = 2979
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 106.949                  try = 2980
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 116.16900000000003       try = 2981
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 106.7112                 try = 2982
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 106.87800000000001       try = 2983
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 96.32480000000001        try = 2984
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 115.04370000000002       try = 2985
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 106.43470000000002       try = 2986
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 107.12910000000001       try = 2987
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 97.42469999999999        try = 2988
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 106.65430000000002       try = 2989
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 96.37190000000001        try = 2990
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 96.6421                  try = 2991
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 85.26429999999999        try = 2992
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 136.2551                 try = 2993
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 119.19930000000001       try = 2994
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 120.22310000000002       try = 2995
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 102.07190000000001       try = 2996
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 120.76470000000003       try = 2997
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 102.03550000000003       try = 2998
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 102.63510000000002       try = 2999
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 82.81050000000002        try = 3000
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 119.20360000000002       try = 3001
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 101.32320000000003       try = 3002
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 102.45040000000003       try = 3003
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 83.47460000000001        try = 3004
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 102.17700000000004       try = 3005
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 82.62320000000003        try = 3006
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 83.32620000000001        try = 3007
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 62.67699999999999        try = 3008
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 124.49330000000002       try = 3009
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 115.98770000000002       try = 3010
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 116.42050000000002       try = 3011
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 106.8195                 try = 3012
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 117.11950000000003       try = 3013
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 106.94050000000001       try = 3014
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 106.94910000000002       try = 3015
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 95.6747                  try = 3016
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 115.72440000000003       try = 3017
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 106.39420000000003       try = 3018
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 106.93040000000002       try = 3019
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 96.5048                  try = 3020
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 106.81440000000003       try = 3021
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 95.81080000000003        try = 3022
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 95.92280000000002        try = 3023
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 83.8238                  try = 3024
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 137.8428                 try = 3025
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 120.06580000000001       try = 3026
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 120.93140000000001       try = 3027
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 102.059                  try = 3028
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 121.83180000000003       try = 3029
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 102.38140000000001       try = 3030
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 102.82280000000002       try = 3031
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 82.277                   try = 3032
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 120.00090000000003       try = 3033
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 101.39930000000003       try = 3034
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 102.36830000000002       try = 3035
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 82.67130000000002        try = 3036
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 102.45370000000003       try = 3037
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 82.17870000000002        try = 3038
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 82.72350000000002        try = 3039
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 61.353100000000005       try = 3040
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 144.92249999999999       try = 3041
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 124.10430000000001       try = 3042
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 125.0785                 try = 3043
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 103.16489999999999       try = 3044
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 125.32090000000001       try = 3045
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 102.82930000000002       try = 3046
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 103.3793                 try = 3047
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 79.79229999999998        try = 3048
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 123.97320000000002       try = 3049
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 102.3304                 try = 3050
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 103.408                  try = 3051
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 80.6698                  try = 3052
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 102.83540000000002       try = 3053
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 79.51919999999998        try = 3054
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 80.1726                  try = 3055
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 55.760999999999996       try = 3056
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 152.9018                 try = 3057
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 122.81220000000002       try = 3058
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 124.2192                 try = 3059
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 93.0342                  try = 3060
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 124.66300000000001       try = 3061
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 92.9                     try = 3062
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 93.8828                  try = 3063
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 61.0244                  try = 3064
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 122.87950000000002       try = 3065
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 91.9653                  try = 3066
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 93.4757                  try = 3067
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 61.4661                  try = 3068
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 93.10450000000002        try = 3069
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 60.51689999999999        try = 3070
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 61.603100000000005       try = 3071
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 27.920099999999998       try = 3072
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 53.95469999999999        try = 3073
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 78.3339                  try = 3074
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 77.6745                  try = 3075
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 100.95830000000001       try = 3076
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 78.4631                  try = 3077
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 101.16890000000002       try = 3078
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 100.0853                 try = 3079
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 121.6957                 try = 3080
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 77.83519999999999        try = 3081
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 101.3898                 try = 3082
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 100.8338                 try = 3083
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 123.293                  try = 3084
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 100.8074                 try = 3085
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 122.68860000000001       try = 3086
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 121.70839999999997       try = 3087
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 142.49419999999998       try = 3088
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 79.5064                  try = 3089
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 94.6142                  try = 3090
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 94.3876                  try = 3091
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.40000000000002       try = 3092
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 95.37760000000002        try = 3093
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.81200000000003       try = 3094
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.16120000000002       try = 3095
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 120.5002                 try = 3096
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 94.3139                  try = 3097
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.59710000000003       try = 3098
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.4739                 try = 3099
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 121.6617                 try = 3100
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.64890000000001       try = 3101
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 121.25870000000002       try = 3102
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 120.7113                 try = 3103
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 132.22570000000002       try = 3104
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 83.5407                  try = 3105
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 95.60730000000002        try = 3106
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 95.48930000000001        try = 3107
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 106.46050000000001       try = 3108
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 95.82130000000001        try = 3109
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 106.21450000000002       try = 3110
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 105.6723                 try = 3111
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 114.9701                 try = 3112
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 95.24080000000001        try = 3113
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 106.48280000000001       try = 3114
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 106.4682                 try = 3115
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 116.6148                 try = 3116
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 105.9852                 try = 3117
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 115.55380000000001       try = 3118
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 115.11500000000001       try = 3119
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 123.58819999999997       try = 3120
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 103.72220000000003       try = 3121
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 106.51740000000004       try = 3122
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 106.83220000000003       try = 3123
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.53200000000001       try = 3124
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 107.36560000000003       try = 3125
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.48740000000001       try = 3126
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.37800000000001       try = 3127
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.40440000000002       try = 3128
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 106.34930000000001       try = 3129
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.3199                 try = 3130
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.7381                 try = 3131
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 109.6133                 try = 3132
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.4565                 try = 3133
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.75370000000001       try = 3134
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.7477                 try = 3135
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 107.9495                 try = 3136
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 84.6472                  try = 3137
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 95.9926                  try = 3138
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 95.7164                  try = 3139
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 105.9664                 try = 3140
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 96.4072                  try = 3141
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 106.0792                 try = 3142
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 105.3788                 try = 3143
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 113.95539999999998       try = 3144
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 95.5569                  try = 3145
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 106.0777                 try = 3146
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 105.90489999999998       try = 3147
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 115.33029999999998       try = 3148
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 105.7807                 try = 3149
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 114.62809999999999       try = 3150
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 114.03109999999997       try = 3151
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 121.78309999999998       try = 3152
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 104.9453                 try = 3153
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 107.01930000000002       try = 3154
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 107.17590000000001       try = 3155
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.1545                 try = 3156
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.0681                 try = 3157
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.46870000000001       try = 3158
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.2011                 try = 3159
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 107.5063                 try = 3160
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 106.78200000000001       try = 3161
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.0314                 try = 3162
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.29139999999998       try = 3163
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.44539999999999       try = 3164
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 108.36859999999999       try = 3165
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 107.94460000000001       try = 3166
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 107.78039999999999       try = 3167
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 106.26099999999998       try = 3168
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 111.79180000000001       try = 3169
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 110.82460000000002       try = 3170
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 111.08980000000001       try = 3171
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 109.02720000000001       try = 3172
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 111.32400000000003       try = 3173
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 108.6834                 try = 3174
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 108.5244                 try = 3175
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 104.78840000000002       try = 3176
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 110.5211                 try = 3177
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 108.72930000000002       try = 3178
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 109.0979                 try = 3179
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 106.2107                 try = 3180
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 108.5171                 try = 3181
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 105.0519                 try = 3182
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 104.9963                 try = 3183
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 100.43569999999998       try = 3184
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 126.71970000000002       try = 3185
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 116.48110000000003       try = 3186
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 117.17910000000002       try = 3187
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 105.84510000000002       try = 3188
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 117.61470000000001       try = 3189
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 105.70270000000002       try = 3190
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 105.97650000000002       try = 3191
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 92.9691                  try = 3192
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 116.37600000000002       try = 3193
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 105.31280000000001       try = 3194
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 106.11420000000001       try = 3195
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 93.9556                  try = 3196
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 105.7348                 try = 3197
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 92.9982                  try = 3198
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 93.37539999999998        try = 3199
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 79.54339999999999        try = 3200
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 79.1452                  try = 3201
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 92.9036                  try = 3202
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 92.6866                  try = 3203
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 105.34960000000001       try = 3204
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 93.2806                  try = 3205
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 105.3656                 try = 3206
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 104.72439999999999       try = 3207
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 115.714                  try = 3208
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 92.5167                  try = 3209
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 105.4505                 try = 3210
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 105.33689999999999       try = 3211
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 117.17529999999998       try = 3212
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 105.1159                 try = 3213
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 116.37629999999999       try = 3214
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 115.83849999999998       try = 3215
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 126.00349999999997       try = 3216
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 101.06930000000001       try = 3217
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 105.55630000000002       try = 3218
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 105.77210000000001       try = 3219
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 109.1637                 try = 3220
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 106.56750000000002       try = 3221
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 109.3811                 try = 3222
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 109.1727                 try = 3223
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 110.89090000000002       try = 3224
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 105.36780000000002       try = 3225
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 109.0302                 try = 3226
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 109.34939999999997       try = 3227
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.9164                 try = 3228
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 109.3298                 try = 3229
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.3188                 try = 3230
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.21379999999999       try = 3231
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 112.1074                 try = 3232
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 106.48620000000001       try = 3233
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 107.93200000000002       try = 3234
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.2564                 try = 3235
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.60679999999999       try = 3236
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.39380000000001       try = 3237
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.1662                 try = 3238
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.0664                 try = 3239
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 106.74340000000001       try = 3240
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 107.6773                 try = 3241
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.2985                 try = 3242
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.72629999999998       try = 3243
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.25209999999997       try = 3244
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.0487                 try = 3245
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 106.9965                 try = 3246
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 107.00009999999997       try = 3247
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 104.85249999999998       try = 3248
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 123.04010000000001       try = 3249
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 115.21450000000002       try = 3250
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 115.97170000000001       try = 3251
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 107.0507                 try = 3252
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 116.3105                 try = 3253
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 106.81150000000002       try = 3254
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 107.14450000000001       try = 3255
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 96.55009999999999        try = 3256
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 115.1582                 try = 3257
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 106.508                  try = 3258
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 107.36859999999999       try = 3259
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 97.62299999999998        try = 3260
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 106.8924                 try = 3261
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 96.5688                  try = 3262
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 97.00519999999999        try = 3263
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 85.58619999999998        try = 3264
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.25310000000002       try = 3265
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.9777                 try = 3266
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 108.14389999999999       try = 3267
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.7731                 try = 3268
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 108.6401                 try = 3269
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.69130000000001       try = 3270
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.43329999999999       try = 3271
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 105.38909999999998       try = 3272
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.65379999999999       try = 3273
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.5538                 try = 3274
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.82339999999998       try = 3275
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 106.62799999999999       try = 3276
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 107.5046                 try = 3277
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 105.73119999999999       try = 3278
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 105.57659999999998       try = 3279
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 102.70779999999998       try = 3280
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 123.92360000000001       try = 3281
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 115.3768                 try = 3282
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 115.97579999999998       try = 3283
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 106.33360000000002       try = 3284
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 116.6734                 try = 3285
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 106.45320000000001       try = 3286
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 106.628                  try = 3287
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 95.3124                  try = 3288
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 115.25129999999999       try = 3289
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 105.87989999999999       try = 3290
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 106.58229999999998       try = 3291
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 96.11549999999997        try = 3292
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 106.46489999999999       try = 3293
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 95.42009999999999        try = 3294
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 95.69829999999999        try = 3295
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 83.55809999999998        try = 3296
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 132.1527                 try = 3297
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 120.56470000000002       try = 3298
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 121.27229999999999       try = 3299
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.5889                 try = 3300
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 121.3119                 try = 3301
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.0505                 try = 3302
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.33389999999999       try = 3303
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 93.97710000000001        try = 3304
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 120.37299999999999       try = 3305
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 107.96039999999999       try = 3306
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.77139999999999       try = 3307
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 95.26339999999999        try = 3308
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 107.996                  try = 3309
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 93.91                    try = 3310
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 94.29679999999998        try = 3311
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 79.11539999999998        try = 3312
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 143.45300000000003       try = 3313
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 122.59360000000001       try = 3314
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 123.734                  try = 3315
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 101.7792                 try = 3316
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 123.97500000000001       try = 3317
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 101.44220000000001       try = 3318
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 102.15839999999999       try = 3319
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 78.53020000000001        try = 3320
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 122.60029999999999       try = 3321
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 100.9163                 try = 3322
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 102.16009999999999       try = 3323
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 79.38069999999999        try = 3324
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 101.58609999999999       try = 3325
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 78.22869999999999        try = 3326
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 79.04829999999998        try = 3327
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 54.59550000000001        try = 3328
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 77.31989999999999        try = 3329
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 93.42389999999999        try = 3330
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 93.12509999999999        try = 3331
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.13370000000002       try = 3332
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 94.09790000000001        try = 3333
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.52850000000004       try = 3334
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 107.80550000000002       try = 3335
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 121.14070000000001       try = 3336
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 93.0592                  try = 3337
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.33860000000003       try = 3338
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.14320000000002       try = 3339
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 122.3272                 try = 3340
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.30100000000003       try = 3341
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 121.90700000000002       try = 3342
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 121.2874                 try = 3343
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 133.798                  try = 3344
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 101.30960000000002       try = 3345
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 108.14220000000005       try = 3346
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 108.27620000000002       try = 3347
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 114.01340000000002       try = 3348
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 109.45040000000003       try = 3349
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 114.60960000000001       try = 3350
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 114.31940000000002       try = 3351
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 118.38320000000002       try = 3352
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 107.97590000000002       try = 3353
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 113.98390000000002       try = 3354
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 114.22130000000001       try = 3355
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 119.13390000000001       try = 3356
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 114.58050000000001       try = 3357
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 118.91510000000001       try = 3358
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 118.72830000000002       try = 3359
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 121.96750000000002       try = 3360
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 101.6069                 try = 3361
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 105.39830000000002       try = 3362
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 105.64090000000002       try = 3363
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.33690000000004       try = 3364
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 106.15710000000001       try = 3365
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.27510000000005       try = 3366
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.09350000000003       try = 3367
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.11610000000003       try = 3368
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 105.1658                 try = 3369
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.13260000000004       try = 3370
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.47860000000003       try = 3371
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.35000000000001       try = 3372
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.17980000000003       try = 3373
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.47320000000002       try = 3374
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.39500000000002       try = 3375
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.593                  try = 3376
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 120.22640000000003       try = 3377
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 114.74640000000005       try = 3378
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 115.42180000000003       try = 3379
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 108.84640000000003       try = 3380
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 116.13940000000005       try = 3381
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 108.98600000000003       try = 3382
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 109.23720000000003       try = 3383
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 100.98840000000003       try = 3384
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 114.71230000000003       try = 3385
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 108.40770000000003       try = 3386
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 109.18650000000001       try = 3387
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 101.7865                 try = 3388
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 109.08910000000003       try = 3389
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 101.11110000000001       try = 3390
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 101.46570000000001       try = 3391
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 92.39229999999999        try = 3392
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 102.73980000000002       try = 3393
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 105.81                   try = 3394
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 105.8944                 try = 3395
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 107.86920000000002       try = 3396
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 106.7694                 try = 3397
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 108.16620000000002       try = 3398
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 107.8264                 try = 3399
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 108.12780000000001       try = 3400
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 105.50830000000002       try = 3401
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 107.75390000000003       try = 3402
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 107.94170000000001       try = 3403
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 109.0919                 try = 3404
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 108.00170000000003       try = 3405
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 108.5739                 try = 3406
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 108.3375                 try = 3407
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 107.81429999999997       try = 3408
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 121.47590000000001       try = 3409
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 115.27470000000001       try = 3410
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 115.79190000000001       try = 3411
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 108.49530000000001       try = 3412
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 116.86830000000002       try = 3413
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 108.9937                 try = 3414
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 109.08670000000001       try = 3415
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 100.1167                 try = 3416
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 115.17140000000002       try = 3417
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 108.1456                 try = 3418
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 108.76619999999998       try = 3419
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 100.645                  try = 3420
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 109.0276                 try = 3421
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 100.3284                 try = 3422
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 100.5248                 try = 3423
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 90.7302                  try = 3424
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 124.58540000000002       try = 3425
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 115.34300000000003       try = 3426
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 115.96880000000002       try = 3427
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 105.63100000000001       try = 3428
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 116.38720000000002       try = 3429
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 105.47140000000002       try = 3430
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 105.673                  try = 3431
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 93.66180000000001        try = 3432
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 115.17350000000002       try = 3433
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 105.10650000000001       try = 3434
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 105.8357                 try = 3435
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 94.6733                  try = 3436
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 105.43910000000001       try = 3437
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 93.6987                  try = 3438
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 94.0037                  try = 3439
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 81.16789999999999        try = 3440
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 137.95130000000003       try = 3441
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 119.43750000000003       try = 3442
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 120.49610000000001       try = 3443
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 100.88690000000001       try = 3444
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 121.11590000000001       try = 3445
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 100.92870000000002       try = 3446
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 101.56310000000002       try = 3447
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 80.2805                  try = 3448
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 119.46640000000001       try = 3449
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 100.12800000000001       try = 3450
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 101.29                   try = 3451
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 80.8562                  try = 3452
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 101.09480000000002       try = 3453
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 80.083                   try = 3454
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 80.82079999999999        try = 3455
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 58.7136                  try = 3456
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 99.28540000000001        try = 3457
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 104.76860000000003       try = 3458
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 104.91220000000001       try = 3459
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 109.30000000000004       try = 3460
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 105.69040000000003       try = 3461
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 109.50020000000004       try = 3462
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 109.21960000000003       try = 3463
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 111.93400000000001       try = 3464
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 104.51570000000002       try = 3465
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 109.17430000000003       try = 3466
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 109.42130000000003       try = 3467
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 112.98450000000001       try = 3468
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 109.38450000000003       try = 3469
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 112.36970000000002       try = 3470
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 112.19250000000002       try = 3471
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 114.0823                 try = 3472
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 119.64750000000004       try = 3473
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 115.85930000000005       try = 3474
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 116.43570000000003       try = 3475
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 111.55210000000004       try = 3476
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 117.41530000000004       try = 3477
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 111.95370000000003       try = 3478
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 112.10590000000003       try = 3479
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 105.54890000000002       try = 3480
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 115.80480000000003       try = 3481
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 111.19200000000004       try = 3482
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 111.87180000000002       try = 3483
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 106.1636                 try = 3484
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 112.03640000000003       try = 3485
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 105.75020000000002       try = 3486
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 106.00580000000001       try = 3487
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 98.62420000000002        try = 3488
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 121.32740000000003       try = 3489
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 114.49800000000003       try = 3490
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 115.18300000000004       try = 3491
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 107.25820000000003       try = 3492
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 115.50460000000004       try = 3493
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 107.00180000000002       try = 3494
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 107.26260000000002       try = 3495
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 97.66440000000001        try = 3496
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 114.37730000000003       try = 3497
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 106.72330000000002       try = 3498
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 107.51170000000002       try = 3499
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 98.76230000000001        try = 3500
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 107.01830000000001       try = 3501
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 97.69090000000001        try = 3502
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 98.05510000000001        try = 3503
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 87.6323                  try = 3504
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 136.31930000000003       try = 3505
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 120.21850000000002       try = 3506
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 121.33630000000004       try = 3507
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 104.14010000000003       try = 3508
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 121.85930000000003       try = 3509
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 104.08510000000003       try = 3510
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 104.77870000000003       try = 3511
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 85.90910000000004        try = 3512
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 120.29620000000001       try = 3513
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 103.37080000000002       try = 3514
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 104.59200000000001       try = 3515
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 86.57120000000002        try = 3516
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 104.30000000000003       try = 3517
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 85.70120000000001        try = 3518
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 86.49820000000001        try = 3519
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 66.80399999999999        try = 3520
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 122.12070000000003       try = 3521
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 114.57010000000004       try = 3522
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 115.09690000000003       try = 3523
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 106.45090000000002       try = 3524
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 115.77730000000003       try = 3525
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 106.55330000000002       try = 3526
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 106.65590000000002       try = 3527
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 96.33650000000002        try = 3528
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 114.38020000000003       try = 3529
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 106.00500000000002       try = 3530
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 106.63520000000001       try = 3531
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 97.16460000000002        try = 3532
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 106.50060000000002       try = 3533
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 96.45200000000001        try = 3534
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 96.65800000000002        try = 3535
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 85.51400000000001        try = 3536
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 137.22920000000002       try = 3537
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 120.40720000000002       try = 3538
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 121.36680000000001       try = 3539
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 103.44940000000003       try = 3540
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 122.24860000000002       try = 3541
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 103.7532                 try = 3542
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 104.28860000000002       try = 3543
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 84.69780000000002        try = 3544
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 120.41570000000002       try = 3545
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 102.76910000000001       try = 3546
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 103.83210000000001       try = 3547
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 85.0901                  try = 3548
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 103.89890000000001       try = 3549
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 84.5789                  try = 3550
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 85.21770000000001        try = 3551
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 64.8023                  try = 3552
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 141.7213                 try = 3553
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 121.85810000000002       try = 3554
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 122.92630000000001       try = 3555
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 101.96770000000002       try = 3556
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 123.15010000000001       try = 3557
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 101.61350000000002       try = 3558
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 102.25750000000002       try = 3559
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 79.6255                  try = 3560
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 121.80040000000002       try = 3561
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 101.11260000000001       try = 3562
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 102.28420000000001       try = 3563
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 80.501                   try = 3564
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 101.69300000000001       try = 3565
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 79.3318                  try = 3566
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 80.0792                  try = 3567
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 56.6226                  try = 3568
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 151.45960000000002       try = 3569
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 122.325                  try = 3570
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 123.82600000000001       try = 3571
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 93.59600000000002        try = 3572
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 124.25120000000001       try = 3573
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 93.4432                  try = 3574
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 94.52000000000001        try = 3575
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 62.61659999999999        try = 3576
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 122.4657                 try = 3577
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 92.5065                  try = 3578
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 94.1109                  try = 3579
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 63.0563                  try = 3580
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 93.72109999999999        try = 3581
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 62.08849999999998        try = 3582
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 63.26869999999999        try = 3583
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 30.5407                  try = 3584
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 79.96759999999999        try = 3585
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 93.2292                  try = 3586
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 92.943                   try = 3587
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 105.10919999999999       try = 3588
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 93.63540000000002        try = 3589
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 105.22360000000002       try = 3590
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 104.5132                 try = 3591
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 115.00599999999999       try = 3592
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 92.7937                  try = 3593
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 105.23070000000001       try = 3594
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 105.0479                 try = 3595
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 116.38949999999997       try = 3596
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 104.92530000000001       try = 3597
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 115.6889                 try = 3598
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 115.08190000000002       try = 3599
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 124.7501                 try = 3600
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 101.61550000000001       try = 3601
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 105.60570000000003       try = 3602
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 105.7523                 try = 3603
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.64710000000001       try = 3604
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 106.64610000000003       try = 3605
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.96290000000002       try = 3606
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.68530000000001       try = 3607
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 109.90670000000003       try = 3608
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 105.3686                 try = 3609
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.53420000000001       try = 3610
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.7842                 try = 3611
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 110.85440000000003       try = 3612
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.86300000000001       try = 3613
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 110.35520000000005       try = 3614
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 110.18100000000003       try = 3615
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 110.5778                 try = 3616
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.07160000000002       try = 3617
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 108.02060000000002       try = 3618
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 108.2758                 try = 3619
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 108.12940000000002       try = 3620
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 108.51160000000002       try = 3621
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.78720000000003       try = 3622
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.61820000000002       try = 3623
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 105.7984                 try = 3624
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.71730000000001       try = 3625
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.84170000000002       try = 3626
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 108.2003                 try = 3627
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.22929999999998       try = 3628
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.62110000000003       try = 3629
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 106.07210000000002       try = 3630
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 106.0065                 try = 3631
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 103.3621                 try = 3632
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 123.34930000000001       try = 3633
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 115.02690000000003       try = 3634
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 115.71490000000001       try = 3635
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 106.29710000000001       try = 3636
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 116.15210000000003       try = 3637
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 106.15630000000003       try = 3638
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 106.42010000000002       try = 3639
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 95.32890000000002        try = 3640
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 114.92200000000003       try = 3641
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 105.77500000000002       try = 3642
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 106.56640000000002       try = 3643
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 96.324                   try = 3644
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 106.18860000000002       try = 3645
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 95.36820000000002        try = 3646
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 95.7354                  try = 3647
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 83.81960000000001        try = 3648
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 108.73130000000002       try = 3649
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 108.9591                 try = 3650
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 109.05609999999999       try = 3651
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 108.18849999999999       try = 3652
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 109.6507                 try = 3653
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 108.2051                 try = 3654
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 107.8779                 try = 3655
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 105.3369                 try = 3656
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 108.5866                 try = 3657
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 107.9898                 try = 3658
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 108.19019999999999       try = 3659
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 106.49799999999999       try = 3660
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 107.9698                 try = 3661
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 105.6996                 try = 3662
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 105.47579999999999       try = 3663
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 102.11019999999998       try = 3664
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 125.1256                 try = 3665
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 116.08200000000001       try = 3666
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 116.6118                 try = 3667
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 106.4728                 try = 3668
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 117.40780000000001       try = 3669
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 106.69080000000001       try = 3670
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 106.7964                 try = 3671
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 94.98400000000001        try = 3672
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 115.90790000000001       try = 3673
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 106.03970000000001       try = 3674
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 106.6729                 try = 3675
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 95.70929999999998        try = 3676
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 106.65390000000001       try = 3677
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 95.1123                  try = 3678
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 95.3213                  try = 3679
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 82.6843                  try = 3680
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 133.3939                 try = 3681
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 121.30910000000002       try = 3682
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 121.9475                 try = 3683
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 108.7673                 try = 3684
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 122.08550000000001       try = 3685
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 108.32730000000002       try = 3686
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 108.54150000000001       try = 3687
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 93.6879                  try = 3688
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 121.06880000000001       try = 3689
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 108.1594                 try = 3690
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 108.9012                 try = 3691
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 94.8964                  try = 3692
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 108.22420000000001       try = 3693
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 93.6414                  try = 3694
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 93.959                   try = 3695
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 78.2808                  try = 3696
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 144.41800000000003       try = 3697
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 123.06180000000003       try = 3698
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 124.13300000000002       try = 3699
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 101.68140000000001       try = 3700
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 124.47240000000002       try = 3701
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 101.44280000000002       try = 3702
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 102.08980000000001       try = 3703
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 77.96480000000001        try = 3704
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 123.01990000000002       try = 3705
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 100.83910000000003       try = 3706
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 102.01370000000001       try = 3707
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 78.7375                  try = 3708
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 101.53810000000001       try = 3709
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 77.68390000000001        try = 3710
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 78.4343                  try = 3711
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 53.48470000000001        try = 3712
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 104.22010000000002       try = 3713
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 106.86090000000003       try = 3714
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 107.01710000000001       try = 3715
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.56250000000001       try = 3716
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 107.51490000000003       try = 3717
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.48230000000001       try = 3718
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.21430000000001       try = 3719
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.0863                 try = 3720
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 106.53720000000001       try = 3721
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.35340000000001       try = 3722
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.613                  try = 3723
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 109.3338                 try = 3724
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.29580000000001       try = 3725
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.43860000000002       try = 3726
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.27400000000002       try = 3727
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 107.32140000000001       try = 3728
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 122.24040000000001       try = 3729
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 115.60980000000002       try = 3730
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 116.19880000000002       try = 3731
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.47280000000002       try = 3732
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 116.89800000000001       try = 3733
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.59400000000002       try = 3734
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.75880000000002       try = 3735
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 99.35940000000002        try = 3736
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 115.48450000000001       try = 3737
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.02930000000002       try = 3738
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.72170000000001       try = 3739
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 100.17110000000001       try = 3740
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.60590000000002       try = 3741
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 99.47730000000003        try = 3742
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 99.7455                  try = 3743
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 89.52150000000003        try = 3744
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 129.0791                 try = 3745
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 119.40730000000002       try = 3746
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 120.10490000000001       try = 3747
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 109.33770000000003       try = 3748
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 120.14610000000002       try = 3749
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.80090000000003       try = 3750
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 109.07430000000002       try = 3751
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 96.63370000000002        try = 3752
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 119.21580000000002       try = 3753
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.71940000000002       try = 3754
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 109.52040000000001       try = 3755
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 97.92859999999999        try = 3756
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.74660000000003       try = 3757
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 96.57680000000002        try = 3758
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 96.9536                  try = 3759
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 83.6884                  try = 3760
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 141.7292                 try = 3761
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 122.78600000000003       try = 3762
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 123.91640000000002       try = 3763
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 103.87780000000002       try = 3764
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 124.15900000000003       try = 3765
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 103.54240000000003       try = 3766
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 104.24860000000002       try = 3767
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 82.53660000000002        try = 3768
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 122.79290000000002       try = 3769
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 103.02510000000004       try = 3770
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 104.25890000000003       try = 3771
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 83.39570000000002        try = 3772
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 103.68650000000002       try = 3773
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 82.24530000000003        try = 3774
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 83.05490000000002        try = 3775
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 60.518299999999996       try = 3776
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 130.3992                 try = 3777
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 120.00620000000002       try = 3778
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 120.54560000000001       try = 3779
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 109.05720000000001       try = 3780
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 120.94560000000001       try = 3781
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 108.87920000000001       try = 3782
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 108.9944                 try = 3783
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 95.8326                  try = 3784
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 119.74550000000002       try = 3785
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 108.52790000000002       try = 3786
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 109.1707                 try = 3787
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 96.85770000000001        try = 3788
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 108.7557                 try = 3789
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 95.86470000000001        try = 3790
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 96.08330000000001        try = 3791
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 82.09690000000002        try = 3792
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 143.1659                 try = 3793
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 123.50150000000002       try = 3794
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 124.47370000000001       try = 3795
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 103.71390000000001       try = 3796
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 125.07510000000002       try = 3797
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 103.73730000000002       try = 3798
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 104.28530000000002       try = 3799
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 81.85210000000001        try = 3800
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 123.43920000000001       try = 3801
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 102.95020000000002       try = 3802
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 104.02580000000002       try = 3803
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 82.44140000000002        try = 3804
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 103.81220000000002       try = 3805
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 81.64980000000001        try = 3806
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 82.3012                  try = 3807
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 59.0434                  try = 3808
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 152.8168                 try = 3809
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 130.11120000000003       try = 3810
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 131.192                  try = 3811
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 107.39100000000002       try = 3812
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 131.13540000000003       try = 3813
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 106.75640000000001       try = 3814
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 107.41300000000001       try = 3815
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 81.93860000000001        try = 3816
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 129.98270000000002       try = 3817
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 106.45250000000001       try = 3818
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 107.6367                 try = 3819
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 83.0111                  try = 3820
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 106.76510000000002       try = 3821
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 81.56150000000001        try = 3822
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 82.3215                  try = 3823
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 56.02250000000001        try = 3824
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 160.21330000000003       try = 3825
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 128.23630000000003       try = 3826
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 129.7499                 try = 3827
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 96.67750000000001        try = 3828
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 129.89470000000003       try = 3829
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 96.24430000000001        try = 3830
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 97.33370000000001        try = 3831
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 62.58789999999999        try = 3832
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 128.30620000000002       try = 3833
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 95.50460000000001        try = 3834
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 97.1216                  try = 3835
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 63.224599999999995       try = 3836
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 96.4514                  try = 3837
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 61.9764                  try = 3838
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 63.16919999999999        try = 3839
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 27.598799999999994       try = 3840
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 99.78880000000002        try = 3841
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 104.77520000000001       try = 3842
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 104.84960000000001       try = 3843
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 108.7406                 try = 3844
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 105.7262                 try = 3845
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 109.03920000000001       try = 3846
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 108.68939999999999       try = 3847
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 110.907                  try = 3848
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 104.47370000000001       try = 3849
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 108.63550000000001       try = 3850
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 108.81329999999998       try = 3851
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 111.87970000000001       try = 3852
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 108.87490000000001       try = 3853
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 111.36330000000002       try = 3854
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 111.11690000000002       try = 3855
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 112.5099                 try = 3856
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 119.8747                 try = 3857
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 115.58970000000001       try = 3858
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 116.0969                 try = 3859
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 110.71650000000001       try = 3860
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 117.17490000000001       try = 3861
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 111.21650000000002       try = 3862
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 111.29950000000001       try = 3863
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 104.2457                 try = 3864
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 115.48660000000001       try = 3865
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 110.37700000000002       try = 3866
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 110.98760000000001       try = 3867
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 104.7826                 try = 3868
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 111.25060000000002       try = 3869
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 104.46760000000003       try = 3870
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 104.65400000000002       try = 3871
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 96.77560000000001        try = 3872
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 121.59379999999999       try = 3873
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 114.26760000000002       try = 3874
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 114.8834                 try = 3875
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 106.4618                 try = 3876
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 115.30340000000001       try = 3877
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 106.30380000000001       try = 3878
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 106.4954                 try = 3879
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 96.4004                  try = 3880
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 114.0983                 try = 3881
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 105.94750000000002       try = 3882
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 106.6667                 try = 3883
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 97.42049999999999        try = 3884
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 106.27170000000001       try = 3885
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 96.44750000000002        try = 3886
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 96.7425                  try = 3887
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 85.82289999999999        try = 3888
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 136.3095                 try = 3889
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 119.71190000000003       try = 3890
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 120.76050000000002       try = 3891
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 103.06750000000001       try = 3892
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 121.38190000000002       try = 3893
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 103.11090000000003       try = 3894
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 103.73530000000001       try = 3895
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 84.36890000000001        try = 3896
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 119.74100000000003       try = 3897
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 102.31880000000002       try = 3898
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 103.47080000000001       try = 3899
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 84.95320000000001        try = 3900
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 103.27720000000004       try = 3901
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 84.1816                  try = 3902
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 84.90939999999999        try = 3903
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 64.7184                  try = 3904
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 123.2799                 try = 3905
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 115.2325                 try = 3906
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 115.69009999999999       try = 3907
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 106.54729999999999       try = 3908
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 116.4689                 try = 3909
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 106.74810000000001       try = 3910
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 106.7815                 try = 3911
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 95.9653                  try = 3912
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 114.994                  try = 3913
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 106.12200000000001       try = 3914
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 106.68299999999999       try = 3915
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 96.7156                  try = 3916
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 106.64680000000001       try = 3917
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 96.10140000000001        try = 3918
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 96.2382                  try = 3919
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 84.5974                  try = 3920
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 138.1122                 try = 3921
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 120.7934                 try = 3922
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 121.6838                 try = 3923
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 103.2696                 try = 3924
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 122.664                  try = 3925
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 103.6718                 try = 3926
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 104.13799999999999       try = 3927
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 84.0504                  try = 3928
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 120.75330000000001       try = 3929
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 102.60990000000001       try = 3930
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 103.6037                 try = 3931
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 84.36489999999999        try = 3932
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 103.7689                 try = 3933
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 83.9521                  try = 3934
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 84.5217                  try = 3935
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 63.6095                  try = 3936
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 142.6435                 try = 3937
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 122.28350000000002       try = 3938
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 123.2825                 try = 3939
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 101.8271                 try = 3940
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 123.60470000000001       try = 3941
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 101.57130000000001       try = 3942
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 102.14609999999999       try = 3943
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 79.01729999999999        try = 3944
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 122.17720000000001       try = 3945
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 100.99260000000001       try = 3946
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 102.095                  try = 3947
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 79.815                   try = 3948
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 101.6022                 try = 3949
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 78.74419999999999        try = 3950
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 79.42239999999998        try = 3951
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 55.469                   try = 3952
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 152.1056                 try = 3953
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 122.47420000000001       try = 3954
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 123.906                  try = 3955
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 93.17920000000001        try = 3956
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 124.42960000000002       try = 3957
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 93.12480000000001        try = 3958
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 94.13239999999999        try = 3959
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 61.73219999999999        try = 3960
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 122.56630000000001       try = 3961
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 92.11030000000001        try = 3962
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 93.6455                  try = 3963
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 62.09409999999999        try = 3964
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 93.3541                  try = 3965
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 61.22469999999999        try = 3966
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 62.335699999999996       try = 3967
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 29.1109                  try = 3968
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 120.81630000000001       try = 3969
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 115.18190000000003       try = 3970
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 115.6987                 try = 3971
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 108.96890000000002       try = 3972
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 116.3807                 try = 3973
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 109.07290000000002       try = 3974
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 109.16550000000001       try = 3975
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 100.76230000000002       try = 3976
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 114.99220000000001       try = 3977
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 108.53320000000002       try = 3978
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 109.1534                 try = 3979
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 101.59900000000002       try = 3980
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 109.02040000000001       try = 3981
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 100.88800000000003       try = 3982
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 101.08400000000002       try = 3983
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 91.85620000000003        try = 3984
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 137.2746                 try = 3985
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 122.36880000000004       try = 3986
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 123.31840000000003       try = 3987
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 107.31720000000001       try = 3988
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 124.20180000000003       try = 3989
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 107.62260000000003       try = 3990
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 108.14800000000001       try = 3991
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 90.47340000000001        try = 3992
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 122.37750000000003       try = 3993
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 106.64710000000002       try = 3994
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 107.70010000000002       try = 3995
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 90.87430000000002        try = 3996
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 107.76850000000003       try = 3997
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 90.36470000000003        try = 3998
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 90.99350000000001        try = 3999
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 72.49430000000001        try = 4000
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 140.3763                 try = 4001
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 122.42930000000003       try = 4002
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 123.48750000000003       try = 4003
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 104.44510000000001       try = 4004
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 123.71290000000002       try = 4005
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 104.09250000000002       try = 4006
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 104.7265                 try = 4007
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 84.0107                  try = 4008
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 122.37180000000004       try = 4009
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 103.6002                 try = 4010
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 104.76180000000001       try = 4011
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 84.8948                  try = 4012
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 104.17220000000002       try = 4013
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 83.7272                  try = 4014
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 84.46459999999999        try = 4015
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 62.924199999999985       try = 4016
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 151.4644                 try = 4017
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 124.24600000000002       try = 4018
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 125.73700000000002       try = 4019
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 97.42320000000002        try = 4020
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 126.16380000000004       try = 4021
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 97.27200000000002        try = 4022
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 98.3388                  try = 4023
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 68.35159999999999        try = 4024
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 124.38690000000004       try = 4025
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 96.3439                  try = 4026
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 97.93830000000001        try = 4027
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 68.7999                  try = 4028
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 97.5501                  try = 4029
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 67.8337                  try = 4030
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 69.00389999999999        try = 4031
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 38.192099999999996       try = 4032
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 141.72279999999998       try = 4033
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 123.05460000000004       try = 4034
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 123.95460000000003       try = 4035
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 104.191                  try = 4036
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 124.53880000000002       try = 4037
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 104.19720000000001       try = 4038
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 104.673                  try = 4039
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 83.236                   try = 4040
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 122.92790000000004       try = 4041
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 103.43510000000002       try = 4042
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 104.4385                 try = 4043
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 83.85030000000002        try = 4044
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 104.20770000000002       try = 4045
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 83.04150000000001        try = 4046
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 83.6207                  try = 4047
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 61.359100000000005       try = 4048
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 152.92750000000004       try = 4049
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 124.98790000000002       try = 4050
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 126.32070000000002       try = 4051
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 97.28570000000002        try = 4052
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 127.10630000000003       try = 4053
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 97.49330000000002        try = 4054
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 98.4019                  try = 4055
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 67.6935                  try = 4056
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 125.05960000000003       try = 4057
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 96.29540000000003        try = 4058
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 97.73160000000001        try = 4059
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 67.87200000000001        try = 4060
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 97.70220000000002        try = 4061
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 67.2646                  try = 4062
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 68.2766                  try = 4063
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 36.743599999999994       try = 4064
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 158.84140000000002       try = 4065
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 127.86060000000003       try = 4066
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 129.30200000000002       try = 4067
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 97.2258                  try = 4068
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 129.42960000000002       try = 4069
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 96.7754                  try = 4070
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 97.7926                  try = 4071
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 64.043                   try = 4072
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 127.86610000000003       try = 4073
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 96.06070000000001        try = 4074
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 97.60549999999999        try = 4075
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 64.7047                  try = 4076
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 96.91810000000001        try = 4077
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 63.439299999999996       try = 4078
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 64.5599                  try = 4079
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 29.985699999999998       try = 4080
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 164.67590000000004       try = 4081
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 124.42370000000003       try = 4082
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 126.29790000000003       try = 4083
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 84.95030000000001        try = 4084
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 126.62690000000003       try = 4085
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 84.70130000000002        try = 4086
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 86.1513                  try = 4087
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 43.1303                  try = 4088
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 124.62760000000003       try = 4089
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 83.55080000000002        try = 4090
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 85.5284                  try = 4091
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 43.356199999999994       try = 4092
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 85.0424                  try = 4093
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 42.2922                  try = 4094
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 43.84559999999999        try = 4095
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 0.0                      try = 4096

Best case(solution) = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 164.67590000000004
In [60]:
draw_graph(G, colors_brute, pos)

Method 2: QAOA¶

In [61]:
from scipy.optimize import minimize
from tqdm import tqdm

expectation = get_expectation(G)
p = 64
res = []
for i in tqdm(range(1, p+1)):
    res.append(minimize(expectation, np.ones(i*2)*np.pi/2,
               method='COBYLA', options={'maxiter': 2500}))

100%|██████████| 64/64 [1:45:21<00:00, 98.77s/it]
In [62]:
approx = []
for i in range(p):
    approx.append(-res[i].fun/best_cost_brute)

x = np.arange(1, p+1, 1)

plt.plot(x, approx, marker='+', c='k', linestyle='--')
plt.ylim((0.5, 1))
plt.xlim(0, p+1)
plt.xlabel('p')
plt.ylabel('Approximation')
plt.grid(True)
plt.show()
In [63]:
best_p = np.argmax(approx)
print("The best p(iterationo number) is", best_p)

The best p(iterationo number) is 29
In [64]:
res[best_p].x
Out[64]:
array([2.52689485, 1.57268173, 1.55695347, 2.81099188, 1.56362648,
       1.5748552 , 1.56788115, 1.56132561, 2.56377173, 1.55484819,
       1.57875454, 1.55792987, 2.54669036, 2.54509814, 1.64664937,
       1.51162994, 1.5631047 , 1.58801906, 1.58363122, 1.56403478,
       1.58032027, 1.56055946, 1.56331431, 1.58055344, 1.55799606,
       1.57708116, 1.79944614, 1.70046129, 1.58980492, 1.58179457,
       1.57846946, 1.56581295, 1.56741151, 1.56408914, 1.6611432 ,
       1.48201128, 1.5706365 , 1.57271689, 1.56196477, 1.56606955,
       1.56842419, 1.5632592 , 1.56654433, 1.57072746, 1.56766746,
       1.56782994, 1.56705577, 1.52509944, 1.60553081, 1.55165147,
       1.56727064, 1.58086755, 1.55988022, 1.54581231, 1.5616982 ,
       1.57831815, 1.62978881, 1.50705347, 1.71863255, 1.59493808])
In [65]:
from qiskit.visualization import plot_histogram
backend = Aer.get_backend('aer_simulator')
backend.shots = 512

qc_res = create_qaoa_circ(G, res[best_p].x)
counts = backend.run(qc_res, seed_simulator=10).result().get_counts()
plot_histogram(counts, figsize=(40, 5), title='512 Shots')
Out[65]:
In [67]:
# # Plot the Quantum Circuit of QAOA
# qc_res.draw(output='mpl', plot_barriers=True).savefig('QAOA_circuit.png', dpi=720)
# qc_res.draw(output='mpl', plot_barriers=True)
In [68]:
# qc_res.draw(output='mpl', plot_barriers=True, fold=-1).savefig('QAOA_circuit(full).png', dpi=720)
# qc_res.draw(output='mpl', plot_barriers=True, fold=-1)
In [69]:
xbest_qaoa = list(map(int, list(max(counts, key=counts.get))))
colors_qaoa = ['g' if xbest_qaoa[i] == 0 else 'c' for i in range(n)]

print('xbest_brute :', xbest_brute)
print('QAOA        :', xbest_qaoa)

xbest_brute : [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]
QAOA        : [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]
In [70]:
draw_graph(G, colors_brute, pos)
In [71]:
draw_graph(G, colors_qaoa, pos)
In [72]:
print('Best solution - Brute Force : ' +
      str(xbest_brute) + ',  cost = ' + str(best_cost_brute))
print('Best solution - QAOA        : ' + str(xbest_qaoa) +
      ',  cost = ' + str(-res[best_p].fun))

Best solution - Brute Force : [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],  cost = 164.67590000000004
Best solution - QAOA        : [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0],  cost = 108.05359882812496
In [73]:
# Visualising the clusters
x = data_iris_qaoa
y = np.array(xbest_brute)

plt.figure(figsize=(12, 8))
plt.scatter(x[y == 0, 0], x[y == 0, 1], s=100, c='purple', label='Cluster A')
plt.scatter(x[y == 1, 0], x[y == 1, 1], s=100, c='orange', label='Cluster B')
plt.title('Clustering using Brute-Force')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

# Plotting the centroids of the clusters
# plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=100, c='red', label='Centroids')
# plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
In [74]:
# Visualising the clusters
x = data_iris_qaoa
y = np.array(xbest_qaoa)

plt.figure(figsize=(12, 8))
plt.scatter(x[y == 0, 0], x[y == 0, 1], s=100, c='purple', label='Cluster A')
plt.scatter(x[y == 1, 0], x[y == 1, 1], s=100, c='orange', label='Cluster B')
plt.title('Clustering using QAOA')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

# Plotting the centroids of the clusters
# plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=100, c='red', label='Centroids')
# plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
In [75]:
# Visualising the clusters
x = data_iris_qaoa
y = np.array(data_iris_qaoa_label)

plt.figure(figsize=(12, 8))
plt.scatter(x[y == 0, 0], x[y == 0, 1], s=100,
            c='purple', label='Cluster A(setosa)')
plt.scatter(x[y == 1, 0], x[y == 1, 1], s=100,
            c='orange', label='Cluster B(versicolor)')
plt.scatter(x[y == 2, 0], x[y == 2, 1], s=100,
            c='orange', label='Cluster B(virginica)')
plt.title('Clustering with True labels')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

# Plotting the centroids of the clusters
# plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=100, c='red', label='Centroids')
# plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))

Comparison with K-means Clustering¶

In [76]:
import os
os.environ["OMP_NUM_THREADS"] = '1'
In [77]:
# Finding the optimum number of clusters for k-means classification
from sklearn.cluster import KMeans
x = data_iris_sample.iloc[:, 0:4]
x
Out[77]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)
14 5.8 4.0 1.2 0.2
15 5.7 4.4 1.5 0.4
27 5.2 3.5 1.5 0.2
33 5.5 4.2 1.4 0.2
114 5.8 2.8 5.1 2.4
117 7.7 3.8 6.7 2.2
118 7.7 2.6 6.9 2.3
125 7.2 3.2 6.0 1.8
126 6.2 2.8 4.8 1.8
130 7.4 2.8 6.1 1.9
140 6.7 3.1 5.6 2.4
141 6.9 3.1 5.1 2.3
In [78]:
# Finding the optimum number of clusters for k-means classification
wcss = []
max_num_cluster = len(data_iris_sample)

for i in range(1, max_num_cluster):
    kmeans = KMeans(n_clusters=i, init='k-means++',
                    max_iter=300, n_init=10, random_state=0)
    kmeans.fit(x)
    wcss.append(kmeans.inertia_)

plt.plot(range(1, max_num_cluster), wcss)
plt.xticks(np.arange(1, max_num_cluster, step=1))  # Set label locations.
plt.title('The elbow method')
plt.xlabel('Number of clusters')
plt.ylabel('Within Cluster Sum of Squares')  # within cluster sum of squares
plt.show()

C:\Users\user1\anaconda3\lib\site-packages\sklearn\cluster\_kmeans.py:1036: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.
  warnings.warn(
In [79]:
num_cluster = 2

kmeans = KMeans(n_clusters=num_cluster, init='k-means++',
                max_iter=300, n_init=10, random_state=0)
y_kmeans = kmeans.fit_predict(x)

x.iloc[0:10, :]

y_kmeans
Out[79]:
array([1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0])
In [80]:
y_kmeans
Out[80]:
array([1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0])
In [81]:
# Visualising the clusters
plt.figure(figsize=(12, 8))
plt.scatter(x.iloc[y_kmeans == 0, 0], x.iloc[y_kmeans ==
            0, 1], s=100, c='purple', label='Cluster A')
plt.scatter(x.iloc[y_kmeans == 1, 0], x.iloc[y_kmeans ==
            1, 1], s=100, c='orange', label='Cluster B')
# plt.scatter(x.iloc[y_kmeans == 2, 0], x.iloc[y_kmeans == 2, 1], s=100, c='green', label='Cluster C')
plt.title('Clustering with K-Means')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))


# Plotting the centroids of the clusters
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[
            :, 1], s=100, marker="v", c='red', label='Centroids')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

Silhoutte Score¶

Code with example¶

In [82]:
from sklearn.cluster import KMeans
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')

np.random.seed(100)
num_data = 50

x11 = np.linspace(0.3, 0.7, 20)
x12 = np.linspace(1.3, 1.8, 15)
x13 = np.linspace(2.4, 3, 15)
x1 = np.concatenate((x11, x12, x13), axis=None)
error = np.random.normal(1, 0.5, num_data)
x2 = 1.5*x1+2+error
In [83]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
plt.scatter(x1, x2, color='k')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [84]:
X = np.stack([x1, x2], axis=1)
init = np.array([[2., 4.], [1., 5.], [2.5, 6.]])

kmeans = KMeans(n_clusters=3, init=init)
kmeans.fit(X)
labels = kmeans.labels_
In [85]:
def get_silhouette_results(X, labels):
    def get_sum_distance(target_x, target_cluster):
        res = np.sum([np.linalg.norm(target_x-x) for x in target_cluster])
        return res

    '''
    각 데이터 포인트를 돌면서 a(i), b(i)를 계산
    그리고 s(i)를 계산한다.
    
    마지막으로 Silhouette(실루엣) Coefficient를 계산한다.
    '''
    uniq_labels = np.unique(labels)
    silhouette_val_list = []
    for i in range(len(labels)):
        target_data = X[i]

        # calculate a(i)
        target_label = labels[i]
        target_cluster_data_idx = np.where(labels == target_label)[0]
        if len(target_cluster_data_idx) == 1:
            silhouette_val_list.append(0)
            continue
        else:
            target_cluster_data = X[target_cluster_data_idx]
            temp1 = get_sum_distance(target_data, target_cluster_data)
            a_i = temp1/(target_cluster_data.shape[0]-1)

        # calculate b(i)
        b_i_list = []
        label_list = uniq_labels[np.unique(labels) != target_label]
        for ll in label_list:
            other_cluster_data_idx = np.where(labels == ll)[0]
            other_cluster_data = X[other_cluster_data_idx]
            temp2 = get_sum_distance(target_data, other_cluster_data)
            temp_b_i = temp2/other_cluster_data.shape[0]
            b_i_list.append(temp_b_i)

        b_i = min(b_i_list)
        s_i = (b_i-a_i)/max(a_i, b_i)
        silhouette_val_list.append(s_i)

    silhouette_coef_list = []
    for ul in uniq_labels:
        temp3 = np.mean(
            [s for s, l in zip(silhouette_val_list, labels) if l == ul])
        silhouette_coef_list.append(temp3)

    silhouette_coef = max(silhouette_coef_list)
    return (silhouette_coef, np.array(silhouette_val_list))
In [86]:
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.7434423527756951
In [87]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

Brute Force - Silhoutte Score¶

In [88]:
X = data_iris_qaoa
labels = np.array(xbest_brute)
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.8710026054196033
In [89]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of Brute Force')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

QAOA - Silhoutte Score¶

In [90]:
X = data_iris_qaoa
labels = np.array(xbest_qaoa)
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.3673295355761431
In [91]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of QAOA')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

K-Means - Silhoutte Score¶

In [92]:
X = data_iris_qaoa
labels = y_kmeans
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.8710026054196033
In [93]:
type(xbest_brute)
Out[93]:
list
In [94]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of K-Means')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

True Label- Silhoutte Score¶

In [95]:
data_iris_qaoa_label
data_iris_qaoa_label2 = np.where(
    data_iris_qaoa_label > 1, 1, data_iris_qaoa_label)
data_iris_qaoa_label2
Out[95]:
array([0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1])
In [96]:
X = data_iris_qaoa
labels = data_iris_qaoa_label2
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.8710026054196033
In [97]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of True Label')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()
In [ ]:

Dunn Index¶

In [98]:
import numpy as np
import random
import matplotlib.pyplot as plt

from itertools import combinations

Code with example¶

In [99]:
import numpy as np
import random
import matplotlib.pyplot as plt

from itertools import combinations

np.random.seed(100)
num_data = 20

x1 = np.linspace(0.3, 0.7, num_data)
error = np.random.normal(1, 0.5, num_data)
x2 = 1.5*x1+2+error

X = np.stack([x1, x2], axis=1)
X
Out[99]:
array([[0.3       , 2.57511726],
       [0.32105263, 3.65291915],
       [0.34210526, 4.0896758 ],
       [0.36315789, 3.41851882],
       [0.38421053, 4.06697618],
       [0.40526316, 3.86500416],
       [0.42631579, 3.75006352],
       [0.44736842, 3.13603097],
       [0.46842105, 3.60788366],
       [0.48947368, 3.86171125],
       [0.51052632, 3.53677598],
       [0.53157895, 4.01495017],
       [0.55263158, 3.53714984],
       [0.57368421, 4.26894985],
       [0.59473684, 4.22846567],
       [0.61578947, 3.87147864],
       [0.63684211, 3.68962297],
       [0.65789474, 4.50170845],
       [0.67894737, 3.79935324],
       [0.7       , 3.49084088]])
In [100]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
plt.scatter(x1, x2, color='k')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [ ]:

클러스터 내 거리 측도 Intra-Cluster distance measure¶

  • a. Complete Diameter Distance: This function below calculates the maximum distance between two points within the cluster. (This version was proposed by Dunn).
In [101]:
def complete_diameter_distance(X):
    res = []
    for i, j in combinations(range(X.shape[0]), 2):
        a_i = X[i, :]
        a_j = X[j, :]
        res.append(np.linalg.norm(a_i-a_j))

    return np.max(res)
In [102]:
complete_diameter_distance(X)
Out[102]:
1.9595515390777758
  • b. Average Diamiter Distance: This function calculates the mean distance between all pairs within the same cluster.
In [103]:
def average_diameter_distance(X):
    res = []
    for i, j in combinations(range(X.shape[0]), 2):
        a_i = X[i, :]
        a_j = X[j, :]
        res.append(np.linalg.norm(a_i-a_j))

    return np.mean(res)
In [104]:
average_diameter_distance(X)
Out[104]:
0.5159584769337329
  • c. Average Diamiter Distance: This function calculates distance of all the points from the mean within the cluster.
In [105]:
def centroid_diameter_distance(X):
    center = np.mean(X, axis=0)
    res = 2*np.mean([np.linalg.norm(x-center) for x in X])

    return res
In [106]:
centroid_diameter_distance(X)
Out[106]:
0.6874635793987067

클러스터 간 거리 측도 Inter-Cluster distance measure¶

  • a. Single Linkage Distance: This function below calculates the minimum distance between clusters.
In [107]:
np.random.seed(100)

x11 = np.linspace(0.3, 0.7, 20)
label1 = [0]*len(x11)
x12 = np.linspace(1.3, 1.8, 15)
label2 = [1]*len(x12)
error = np.random.normal(1, 0.5, 35)
x1 = np.concatenate((x11, x12), axis=None)
x2 = 1.5*x1+2+error
labels = label1+label2

X = np.stack((x1, x2), axis=1)

labels = np.array(labels)
X1 = X[np.where(labels == 0)[0], :]
X2 = X[np.where(labels == 1)[0], :]
In [108]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
for i, x in enumerate(X):
    if labels[i] == 0:
        plt.scatter(x[0], x[1], color='blue')
    else:
        plt.scatter(x[0], x[1], color='red')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [109]:
def single_linkage_distance(X1, X2):
    res = []
    for x1 in X1:
        for x2 in X2:
            res.append(np.linalg.norm(x1-x2))
    return np.min(res)
In [110]:
single_linkage_distance(X1, X2)
Out[110]:
0.7724228550378145
  • b. Complete Linkage Distance: This function below calculates the maximum distance between clusters.
In [111]:
def complete_linkage_distance(X1, X2):
    res = []
    for x1 in X1:
        for x2 in X2:
            res.append(np.linalg.norm(x1-x2))
    return np.max(res)
In [112]:
complete_linkage_distance(X1, X2)
Out[112]:
3.807983171195838
  • c. Average Linkage Distance: This function below calculates the minimum distance between clusters.
In [113]:
def average_linkage_distance(X1, X2):
    res = []
    for x1 in X1:
        for x2 in X2:
            res.append(np.linalg.norm(x1-x2))
    return np.mean(res)
In [114]:
average_linkage_distance(X1, X2)
Out[114]:
2.0502961616379003
  • d. Centroid Linkage Distance: This function below calculates distance between centoids of two clusters.
In [115]:
def centroid_linkage_distance(X1, X2):
    center1 = np.mean(X1, axis=0)
    center2 = np.mean(X2, axis=0)
    return np.linalg.norm(center1-center2)
In [116]:
centroid_linkage_distance(X1, X2)
Out[116]:
2.023846293346597
  • e. Average of Centroids Linkage Distance: This function below calculates average value of the distances between a centroid from one cluster and the data points from other clusters.
In [117]:
def average_of_centroids_linkage_distance(X1, X2):
    center1 = np.mean(X1, axis=0)
    center2 = np.mean(X2, axis=0)
    res = []
    for x1 in X1:
        res.append(np.linalg.norm(x1-center2))
    for x2 in X2:
        res.append(np.linalg.norm(x2-center1))

    return np.mean(res)
In [118]:
average_of_centroids_linkage_distance(X1, X2)
Out[118]:
2.035733790732974

Dunn Index 파이썬 구현¶

In [119]:
np.random.seed(100)
num_data = 50

x11 = np.linspace(0.3, 0.7, 20)
label1 = [0]*len(x11)
x12 = np.linspace(1.3, 1.8, 15)
label2 = [1]*len(x12)
x13 = np.linspace(2.4, 3, 15)
label3 = [2]*len(x13)
x1 = np.concatenate((x11, x12, x13), axis=None)
error = np.random.normal(1, 0.5, num_data)
x2 = 1.5*x1+2+error

X = np.stack((x1, x2), axis=1)
labels = np.array(label1+label2+label3)
In [120]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
for i, x in enumerate(X):
    if labels[i] == 0:
        plt.scatter(x[0], x[1], color='blue')
    elif labels[i] == 1:
        plt.scatter(x[0], x[1], color='red')
    else:
        plt.scatter(x[0], x[1], color='green')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [121]:
def Dunn_index(X, labels, intra_cluster_distance_type, inter_cluster_distance_type):
    intra_cdt_dict = {
        'cmpl_dd': complete_diameter_distance,
        'avdd': average_diameter_distance,
        'cent_dd': centroid_diameter_distance
    }
    inter_cdt_dict = {
        'sld': single_linkage_distance,
        'cmpl_ld': complete_linkage_distance,
        'avld': average_linkage_distance,
        'cent_ld': centroid_linkage_distance,
        'av_cent_ld': average_of_centroids_linkage_distance
    }
    # intra cluster distance
    intra_cluster_distance = intra_cdt_dict[intra_cluster_distance_type]

    # inter cluster distance
    inter_cluster_distance = inter_cdt_dict[inter_cluster_distance_type]

    # get minimum value of inter_cluster_distance
    res1 = []
    for i, j in combinations(np.unique(labels), 2):
        X1 = X[np.where(labels == i)[0], :]
        X2 = X[np.where(labels == j)[0], :]
        res1.append(inter_cluster_distance(X1, X2))
    min_inter_cd = np.min(res1)

    # get maximum value of intra_cluser_distance

    res2 = []
    for label in np.unique(labels):
        X_target = X[np.where(labels == label)[0], :]
        if X_target.shape[0] >= 2:
            res2.append(intra_cluster_distance(X_target))
        else:
            res2.append(0)
    max_intra_cd = np.max(res2)

    Dunn_idx = min_inter_cd/max_intra_cd
    return Dunn_idx
In [122]:
intra_cluster_distance_type = ['cmpl_dd', 'avdd', 'cent_dd']
inter_cluster_distance_type = [
    'sld', 'cmpl_ld', 'avld', 'cent_ld', 'av_cent_ld']

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.2780279425885912
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 1.5816104606529293
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 0.7627361333011984
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.7374610426286897
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 0.7486880384584048
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 0.8233205335652861
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.683602504961463
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 2.2586806002025015
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.1838338026300956
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.2170801594919096
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.6140262424157213
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.492995412900513
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.6845069510824404
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.6286867741323774
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.6534816562537682
In [123]:
import random
import pandas as pd

# 빈 DataFrame 생성하기
Dunn_Index_result = pd.DataFrame(
    columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result
Out[123]:
intra cluster inter cluster Dunn index
In [124]:
len(inter_cluster_distance_type)
Out[124]:
5
In [125]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j],
        Dunn_Index_result.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result
Out[125]:
intra cluster inter cluster Dunn index
0 cmpl_dd (sld,) 0.278028
1 cmpl_dd (cmpl_ld,) 1.58161
2 cmpl_dd (avld,) 0.762736
3 cmpl_dd (cent_ld,) 0.737461
4 cmpl_dd (av_cent_ld,) 0.748688
5 avdd (sld,) 0.823321
6 avdd (cmpl_ld,) 4.683603
7 avdd (avld,) 2.258681
8 avdd (cent_ld,) 2.183834
9 avdd (av_cent_ld,) 2.21708
10 cent_dd (sld,) 0.614026
11 cent_dd (cmpl_ld,) 3.492995
12 cent_dd (avld,) 1.684507
13 cent_dd (cent_ld,) 1.628687
14 cent_dd (av_cent_ld,) 1.653482
In [126]:
Dunn_Index_result[Dunn_Index_result['Dunn index']
                  == Dunn_Index_result['Dunn index'].max()]
Out[126]:
intra cluster inter cluster Dunn index
6 avdd (cmpl_ld,) 4.683603
In [ ]:

Brute Force - Dunn Index¶

In [127]:
X = data_iris_qaoa
labels = np.array(xbest_brute)

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.4394867323822669
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.427020798920174
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.916515927431781
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.89065929763941
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.9056927184516308
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 2.6222081260033683
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.421127001549618
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 3.4911774631014354
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 3.444076324044455
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 3.4714616116811077
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.9855602916134834
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.347718333798584
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 2.643551925939384
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.6078865069843116
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.6286229005476347
In [128]:
# 빈 DataFrame 생성하기
Dunn_Index_result_brute = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_brute
Out[128]:
intra cluster inter cluster Dunn index
In [129]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_brute.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_brute.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_brute.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_brute
Out[129]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 1.439487
1 cmpl_dd cmpl_ld 2.427021
2 cmpl_dd avld 1.916516
3 cmpl_dd cent_ld 1.890659
4 cmpl_dd av_cent_ld 1.905693
5 avdd sld 2.622208
6 avdd cmpl_ld 4.421127
7 avdd avld 3.491177
8 avdd cent_ld 3.444076
9 avdd av_cent_ld 3.471462
10 cent_dd sld 1.98556
11 cent_dd cmpl_ld 3.347718
12 cent_dd avld 2.643552
13 cent_dd cent_ld 2.607887
14 cent_dd av_cent_ld 2.628623
In [130]:
Dunn_Index_result_brute[Dunn_Index_result_brute['Dunn index']== Dunn_Index_result_brute['Dunn index'].max()]
Out[130]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 4.421127

QAOA - Dunn Index¶

In [131]:
X = data_iris_qaoa
labels = np.array(xbest_qaoa)

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.07358476872648746
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 1.022392651548532
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 0.6091545196427576
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.4842063189294046
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 0.5556510289377363
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 0.15829313397850517
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.199337441308775
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 1.3103931650560994
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.0416087057421364
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.1952982158014847
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.11321023944547648
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 1.5729521053375464
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 0.9371848307953864
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.7449519004505446
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 0.854869657442073
In [132]:
# 빈 DataFrame 생성하기
Dunn_Index_result_qaoa = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_qaoa
Out[132]:
intra cluster inter cluster Dunn index
In [133]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_qaoa.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_qaoa.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_qaoa.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_qaoa
Out[133]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 0.073585
1 cmpl_dd cmpl_ld 1.022393
2 cmpl_dd avld 0.609155
3 cmpl_dd cent_ld 0.484206
4 cmpl_dd av_cent_ld 0.555651
5 avdd sld 0.158293
6 avdd cmpl_ld 2.199337
7 avdd avld 1.310393
8 avdd cent_ld 1.041609
9 avdd av_cent_ld 1.195298
10 cent_dd sld 0.11321
11 cent_dd cmpl_ld 1.572952
12 cent_dd avld 0.937185
13 cent_dd cent_ld 0.744952
14 cent_dd av_cent_ld 0.85487
In [134]:
Dunn_Index_result_qaoa[Dunn_Index_result_qaoa['Dunn index']== Dunn_Index_result_qaoa['Dunn index'].max()]
Out[134]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 2.199337

K-Means - Dunn Index¶

In [135]:
X = data_iris_qaoa
labels = y_kmeans

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.4394867323822669
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.427020798920174
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.916515927431781
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.89065929763941
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.9056927184516308
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 2.6222081260033683
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.421127001549618
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 3.4911774631014354
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 3.444076324044455
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 3.4714616116811077
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.9855602916134834
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.347718333798584
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 2.643551925939384
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.6078865069843116
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.6286229005476347
In [136]:
# 빈 DataFrame 생성하기
Dunn_Index_result_kmeans = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_kmeans
Out[136]:
intra cluster inter cluster Dunn index
In [137]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_kmeans.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_kmeans.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_kmeans.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_kmeans
Out[137]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 1.439487
1 cmpl_dd cmpl_ld 2.427021
2 cmpl_dd avld 1.916516
3 cmpl_dd cent_ld 1.890659
4 cmpl_dd av_cent_ld 1.905693
5 avdd sld 2.622208
6 avdd cmpl_ld 4.421127
7 avdd avld 3.491177
8 avdd cent_ld 3.444076
9 avdd av_cent_ld 3.471462
10 cent_dd sld 1.98556
11 cent_dd cmpl_ld 3.347718
12 cent_dd avld 2.643552
13 cent_dd cent_ld 2.607887
14 cent_dd av_cent_ld 2.628623
In [138]:
Dunn_Index_result_kmeans[Dunn_Index_result_kmeans['Dunn index']== Dunn_Index_result_kmeans['Dunn index'].max()]
Out[138]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 4.421127

True Label - Dunn Index¶

In [139]:
X = data_iris_qaoa
labels = data_iris_qaoa_label2

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.4394867323822669
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.427020798920174
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.916515927431781
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.89065929763941
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.9056927184516308
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 2.6222081260033683
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.421127001549618
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 3.4911774631014354
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 3.444076324044455
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 3.4714616116811077
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.9855602916134834
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.347718333798584
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 2.643551925939384
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.6078865069843116
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.6286229005476347
In [140]:
# 빈 DataFrame 생성하기
Dunn_Index_result_truelabel = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_truelabel
Out[140]:
intra cluster inter cluster Dunn index
In [141]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_truelabel.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_truelabel.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_truelabel.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_truelabel
Out[141]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 1.439487
1 cmpl_dd cmpl_ld 2.427021
2 cmpl_dd avld 1.916516
3 cmpl_dd cent_ld 1.890659
4 cmpl_dd av_cent_ld 1.905693
5 avdd sld 2.622208
6 avdd cmpl_ld 4.421127
7 avdd avld 3.491177
8 avdd cent_ld 3.444076
9 avdd av_cent_ld 3.471462
10 cent_dd sld 1.98556
11 cent_dd cmpl_ld 3.347718
12 cent_dd avld 2.643552
13 cent_dd cent_ld 2.607887
14 cent_dd av_cent_ld 2.628623
In [142]:
Dunn_Index_result_truelabel[Dunn_Index_result_truelabel['Dunn index']== Dunn_Index_result_truelabel['Dunn index'].max()]
Out[142]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 4.421127
In [143]:
Dunn_Index_results_combined = Dunn_Index_result_brute[['intra cluster', 'inter cluster']]
Dunn_Index_results_combined['Dunn index - Brute'] = Dunn_Index_result_brute['Dunn index']
Dunn_Index_results_combined['Dunn index - QAOA'] = Dunn_Index_result_qaoa['Dunn index']
Dunn_Index_results_combined['Dunn index - K-Means'] = Dunn_Index_result_kmeans['Dunn index']
Dunn_Index_results_combined['Dunn index - True label'] = Dunn_Index_result_truelabel['Dunn index']

Dunn_Index_results_combined
Out[143]:
intra cluster inter cluster Dunn index - Brute Dunn index - QAOA Dunn index - K-Means Dunn index - True label
0 cmpl_dd sld 1.439487 0.073585 1.439487 1.439487
1 cmpl_dd cmpl_ld 2.427021 1.022393 2.427021 2.427021
2 cmpl_dd avld 1.916516 0.609155 1.916516 1.916516
3 cmpl_dd cent_ld 1.890659 0.484206 1.890659 1.890659
4 cmpl_dd av_cent_ld 1.905693 0.555651 1.905693 1.905693
5 avdd sld 2.622208 0.158293 2.622208 2.622208
6 avdd cmpl_ld 4.421127 2.199337 4.421127 4.421127
7 avdd avld 3.491177 1.310393 3.491177 3.491177
8 avdd cent_ld 3.444076 1.041609 3.444076 3.444076
9 avdd av_cent_ld 3.471462 1.195298 3.471462 3.471462
10 cent_dd sld 1.98556 0.11321 1.98556 1.98556
11 cent_dd cmpl_ld 3.347718 1.572952 3.347718 3.347718
12 cent_dd avld 2.643552 0.937185 2.643552 2.643552
13 cent_dd cent_ld 2.607887 0.744952 2.607887 2.607887
14 cent_dd av_cent_ld 2.628623 0.85487 2.628623 2.628623
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